Journal of Geometry and Physics最新文献

{"title":"Jordan algebras over icosahedral cut-and-project quasicrystals","authors":"Daniele Corradetti ,&nbsp;David Chester ,&nbsp;Raymond Aschheim ,&nbsp;Klee Irwin","doi":"10.1016/j.geomphys.2025.105645","DOIUrl":"10.1016/j.geomphys.2025.105645","url":null,"abstract":"<div><div>In this paper we present a general setting for aperiodic Jordan algebras arising from icosahedral quasicrystals that are obtainable as model sets of a cut-and-project scheme with a convex acceptance window. In these hypotheses, we show the existence of an aperiodic Jordan algebra structure whose generators are in one-to-one correspondence with elements of the quasicrystal. Moreover, if the acceptance window enjoys a non-crystallographic symmetry arising from <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><msub><mrow><mi>H</mi></mrow><mrow><mn>3</mn></mrow></msub></math></span> or <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span> then the resulting Jordan algebra enjoys the same <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><msub><mrow><mi>H</mi></mrow><mrow><mn>3</mn></mrow></msub></math></span> or <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span> symmetry. Finally, we present as special cases some examples of Jordan algebras over a Fibonacci-chain quasicrystal, a Penrose tiling, and the Elser-Sloane quasicrystal.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"217 ","pages":"Article 105645"},"PeriodicalIF":1.2,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145104706","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On geometry of turbulent flows","authors":"Valentin Lychagin","doi":"10.1016/j.geomphys.2025.105646","DOIUrl":"10.1016/j.geomphys.2025.105646","url":null,"abstract":"<div><div>In this paper, we apply the method of geometrization of random vectors <span><span>[1]</span></span> to turbulent media, which we understand as random vector fields on base manifolds. This gives rise to various geometric structures on the tangent as well as cotangent bundles. Among these, the most important is the Mahalanobis metric on the tangent bundle, which allows us to obtain all the necessary ingredients for implementing the scheme <span><span>[2]</span></span> to the description of flows in turbulent media. As an illustration, we consider the applications to flows of real gases based on Maxwell–Boltzmann statistics.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"217 ","pages":"Article 105646"},"PeriodicalIF":1.2,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145104707","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Some basic properties of Ricci almost solitons","authors":"Sharief Deshmukh ,&nbsp;Nasser Bin Turki ,&nbsp;Hemangi Madhusudan Shah ,&nbsp;Gabriel-Eduard Vîlcu","doi":"10.1016/j.geomphys.2025.105644","DOIUrl":"10.1016/j.geomphys.2025.105644","url":null,"abstract":"&lt;div&gt;&lt;div&gt;Ricci solitons are stationary solutions of a famous PDE for Riemannian metrics, known under the name of Ricci flow equation. An almost Ricci soliton is a remarkable generalization of Ricci solitons by allowing the soliton constant in Ricci flow equation to be a smooth function. In the present paper, we focuss our study on the most important class of almost Ricci solitons, namely gradient Ricci almost solitons &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; with potential function &lt;em&gt;σ&lt;/em&gt; and associated function &lt;em&gt;f&lt;/em&gt;, abbreviated as &lt;em&gt;GRRAS&lt;/em&gt; &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. On a nontrivial &lt;em&gt;GRRAS&lt;/em&gt; &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, these two functions &lt;em&gt;σ&lt;/em&gt; and &lt;em&gt;f&lt;/em&gt; together with scalar curvature &lt;em&gt;τ&lt;/em&gt; play a significant role. Among the basic properties of a connected &lt;em&gt;GRRAS&lt;/em&gt; &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, it has been observed that there exists a smooth function &lt;em&gt;δ&lt;/em&gt; called the connector of the &lt;em&gt;GRRAS&lt;/em&gt; &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; as it connects the gradients of the potential function &lt;em&gt;σ&lt;/em&gt; and the associated function &lt;em&gt;f&lt;/em&gt;, respectively. In our first result it is shown that a nontrivial &lt;em&gt;GRRAS&lt;/em&gt; &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; with connector &lt;em&gt;δ&lt;/em&gt; gives a generalized soliton, thus establishing an unexpected duality. In our second result, we show that a compact and connected nontrivial &lt;em&gt;GRRAS&lt;/em&gt; &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; with connector &lt;span&gt;&lt;math&gt;&lt;mi&gt;δ&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, for a positive constant &lt;em&gt;c&lt;/em&gt;, and a suitable lower bound on the integral of the Ricci curvature &lt;span&gt;&lt;math&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; is isometric to the &lt;em&gt;n&lt;/em&gt;-sphere &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; and the converse too is shown to hold. In the third result it is established that a ","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"217 ","pages":"Article 105644"},"PeriodicalIF":1.2,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145104705","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the generalized Fourier transform for the modified Hunter-Saxton equation","authors":"Miao-Miao Xie,&nbsp;Shou-Fu Tian,&nbsp;Xing-Jie Yan","doi":"10.1016/j.geomphys.2025.105647","DOIUrl":"10.1016/j.geomphys.2025.105647","url":null,"abstract":"<div><div>In this work, by the squared eigenfunctions of the spectral problem for the modified Hunter-Saxton equation, we derive the generalized Fourier transform and the symplectic basis for the equation. First, we present the symmetry and the asymptotic behavior of the Jost solutions and the scattering data from the inverse scattering transform. Then the completeness relations of the Jost solutions and the squared eigenfunctions are derived by constructing two meromorphic functions, from which we can derive the generalized Fourier transform. Finally, we verified that a set of variables defined by the scattering data and the squared eigenfunctions form the symplectic basis of the phase space, which gives the description in symplectic geometry for the modified Hunter-Saxton equation.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"217 ","pages":"Article 105647"},"PeriodicalIF":1.2,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145094970","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Corrigendum to “Optimal inequalities involving Casorati curvatures along Riemannian maps and Riemannian submersions for Sasakian space forms” [J. Geom. Phys. 210 (2025) 105417]","authors":"Gülistan Polat ,&nbsp;Jae Won Lee ,&nbsp;Bayram Şahin","doi":"10.1016/j.geomphys.2025.105643","DOIUrl":"10.1016/j.geomphys.2025.105643","url":null,"abstract":"","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"217 ","pages":"Article 105643"},"PeriodicalIF":1.2,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145048360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Geodesic orbit metrics on homogeneous spaces arising from generalized flag manifolds with two irreducible summands","authors":"Chao Chen ,&nbsp;Huibin Chen ,&nbsp;Zhiqi Chen","doi":"10.1016/j.geomphys.2025.105641","DOIUrl":"10.1016/j.geomphys.2025.105641","url":null,"abstract":"<div><div>This paper examines invariant geodesic orbit metrics on a class of homogeneous spaces derived from generalized flag manifolds with two irreducible summands. We demonstrate that all invariant geodesic orbit metrics on these homogeneous spaces are naturally reductive.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"217 ","pages":"Article 105641"},"PeriodicalIF":1.2,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145048348","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quantum Wasserstein distances for quantum permutation groups","authors":"Anshu ,&nbsp;David Jekel ,&nbsp;Therese Basa Landry","doi":"10.1016/j.geomphys.2025.105637","DOIUrl":"10.1016/j.geomphys.2025.105637","url":null,"abstract":"<div><div>We seek an analog for the quantum permutation group <span><math><msubsup><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow><mrow><mo>+</mo></mrow></msubsup></math></span> of the normalized Hamming distance for permutations. We define three distances on the tracial state space of <span><math><mi>C</mi><mo>(</mo><msubsup><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>)</mo></math></span> that generalize the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-Wasserstein distance of probability measures on <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> equipped with the normalized Hamming metric, for which we demonstrate basic metric properties, subadditivity under convolution, and density of the Lipschitz elements in the <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-algebra.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"217 ","pages":"Article 105637"},"PeriodicalIF":1.2,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145095163","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"3-Leibniz-Lie triple systems, deformations and cohomologies of nonabelian embedding tensors between Lie triple systems","authors":"Wen Teng","doi":"10.1016/j.geomphys.2025.105638","DOIUrl":"10.1016/j.geomphys.2025.105638","url":null,"abstract":"<div><div>In this paper, first we introduce the notion of nonabelian embedding tensors between Lie triple systems and show that nonabelian embedding tensors induce naturally 3-Leibniz algebras. Next, we introduce the notion of a 3-Leibniz-Lie triple system, which is the underlying algebraic structure of a nonabelian embedding tensor between Lie triple systems. Besides, we construct an <span><math><msub><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span>-algebra whose Maurer-Cartan elements are nonabelian embedding tensors. Then, we have the twisted <span><math><msub><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span>-algebra that governs deformations of nonabelian embedding tensors. Following this, we establish the cohomology of a nonabelian embedding tensor between Lie triple systems and realize it as the cohomology of the descendent 3-Leibniz algebra with coefficients in a suitable representation. As applications, we consider linear deformations of a nonabelian embedding tensor between Lie triple systems and demonstrate that they are governed by the above-established cohomology. Furthermore, the notion of Nijenhuis elements associated with a nonabelian embedding tensor is introduced to characterize trivial linear deformations. Finally, we provide relationships between nonabelian embedding tensors on Lie algebras and associated Lie triple systems.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"217 ","pages":"Article 105638"},"PeriodicalIF":1.2,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145026996","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Unicity problem on meromorphic mappings of complete Kähler manifolds","authors":"Mengyue Liu,&nbsp;Xianjing Dong","doi":"10.1016/j.geomphys.2025.105639","DOIUrl":"10.1016/j.geomphys.2025.105639","url":null,"abstract":"<div><div>Nevanlinna's unicity theorems have always held an important position in value distribution theory. The main purpose of this paper is to generalize the classical Nevanlinna's unicity theorems to non-compact complete Kähler manifolds with either non-positive sectional curvature or nonnegative Ricci curvature.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"217 ","pages":"Article 105639"},"PeriodicalIF":1.2,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145026306","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Eguchi-Hanson harmonic spinors revisited","authors":"Guido Franchetti ,&nbsp;Kirill Krasnov","doi":"10.1016/j.geomphys.2025.105640","DOIUrl":"10.1016/j.geomphys.2025.105640","url":null,"abstract":"<div><div>We revisit the problem of determining the zero modes of the Dirac operator on the Eguchi-Hanson space. It is well known that there are no normalisable zero modes, but such zero modes do appear when the Dirac operator is twisted by a <span><math><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></math></span> connection with <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> normalisable curvature. The main novelty of our treatment is that we use the established formalism of spin-<em>c</em> spinors as complex differential forms, which makes the required calculations remarkably straightforward. In particular, to compute the Dirac operator we never need to compute the spin connection. As a result, we are able to reproduce the known normalisable zero modes of the twisted Eguchi-Hanson Dirac operator by relatively simple computations. We also collect various different descriptions of the Eguchi-Hanson space, including its construction as a hyperkähler quotient of <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>4</mn></mrow></msup></math></span> with the flat metric. The latter illustrates the geometric origin of the connection with <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> curvature used to twist the Dirac operator. To illustrate the power of the formalism developed, we generalise the results to the case of Dirac zero modes on the Ricci-flat Kähler manifolds obtained by applying Calabi's construction to the canonical bundle of <span><math><mi>C</mi><msup><mrow><mi>P</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"217 ","pages":"Article 105640"},"PeriodicalIF":1.2,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145026995","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}