Annals of Global Analysis and Geometry最新文献

{"title":"Existence of conical higher cscK metrics on a minimal ruled surface","authors":"Rajas Sandeep Sompurkar","doi":"10.1007/s10455-026-10046-3","DOIUrl":"10.1007/s10455-026-10046-3","url":null,"abstract":"<div><p>A ‘higher extremal Kähler metric’ is defined (motivated by analogy with the definition of an extremal Kähler metric) as a Kähler metric whose top Chern form equals a globally defined smooth function multiplied by its volume form such that the gradient of the smooth function is a holomorphic vector field. A special case of this kind of metric is a ‘higher constant scalar curvature Kähler (higher cscK) metric’ which is defined (again by analogy with the definition of a constant scalar curvature Kähler (cscK) metric) as one whose top Chern form is a constant multiple of its volume form or equivalently whose top Chern form is harmonic. In our previous paper on higher extremal Kähler metrics we had looked at a certain class of minimal ruled surfaces called as ‘pseudo-Hirzebruch surfaces’ all of which contain two special divisors (viz. the zero and infinity divisors) and serve as the primary example manifolds in the momentum construction method (the Calabi ansatz procedure) which is used for producing explicit examples of the above-mentioned kinds of canonical Kähler metrics. We had proven that every Kähler class on such a surface admits a momentum-constructed higher extremal Kähler metric which is not higher cscK and we had further proven by using the ‘top Bando-Futaki invariant’ that higher cscK metrics do not exist in any Kähler class on the surface. In this paper we will see that if we allow our metrics to develop ‘conical singularities’ along at least one of the two special divisors of the surface then we do get ‘conical higher cscK metrics’ in each Kähler class of the surface by the momentum construction method. We will show that our constructed metrics satisfy the “polyhomogeneous condition” for conical Kähler metrics and we will interpret the conical higher cscK equation “globally on the surface” in terms of the currents of integration along the zero and infinity divisors. We will introduce the ‘top <span>(log )</span> Bando-Futaki invariant’ and then try to prove some standard expected results about it, with the final aim being to employ it to arrive at a certain linear relationship, that we conjecture must exist, between the cone angles of the conical singularities along the zero and infinity divisors.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"69 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148173438","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":"Local index theory for geometric first-order differential operators","authors":"Alberto Richtsfeld","doi":"10.1007/s10455-026-10043-6","DOIUrl":"10.1007/s10455-026-10043-6","url":null,"abstract":"<div><p>We introduce the concept of chiral geometric operators and use Gilkey’s invariance theory to prove the local index theorem for these operators. In other words, we demonstrate that the supertrace of the heat kernel of a given geometric operator converges as time approaches zero and that this limit is the Chern–Weil form of the Atiyah–Singer integrand. In addition to classical Dirac-type operators that appear in geometry, chiral geometric operators include all higher Dirac operators. This includes in particular the Rarita–Schwinger operator. We also construct a new class of such operators on four-manifolds called higher signature operators.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"69 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-026-10043-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148009053","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the curvature and topology of compact stationary spacetimes","authors":"Amir Babak Aazami","doi":"10.1007/s10455-026-10029-4","DOIUrl":"10.1007/s10455-026-10029-4","url":null,"abstract":"<div><p>Using the result of Petersen &amp; Wink ’21, we find obstructions to the curvature and topology of compact Lorentzian manifolds admitting a unit-length timelike Killing vector field.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"69 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147807605","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":"Computer-assisted construction of SU(2)-invariant negative Einstein metrics","authors":"Qiu Shi Wang","doi":"10.1007/s10455-026-10037-4","DOIUrl":"10.1007/s10455-026-10037-4","url":null,"abstract":"<div><p>We construct a 2-parameter family of new triaxial <i>SU</i>(2)-invariant complete negative Einstein metrics on the complex line bundle <span>(mathcal {O}(-4))</span> over <span>(mathbb {C}P^1)</span>. The metrics are conformally compact and neither Kähler nor self-dual. The proof involves using rigorous numerics to produce an approximate Einstein metric to high precision in a bounded region containing the singular orbit or “bolt”, which is then perturbed to a genuine Einstein metric using fixed-point methods. At the boundary of this region, the latter metric is sufficiently close to hyperbolic space for us to show that it indeed extends to a complete, asymptotically hyperbolic Einstein metric.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"69 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-026-10037-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147797022","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Parallel differential forms of codegree two, and three-forms in dimension six","authors":"Andrzej Derdzinski,&nbsp;Paolo Piccione,&nbsp;Ivo Terek","doi":"10.1007/s10455-026-10040-9","DOIUrl":"10.1007/s10455-026-10040-9","url":null,"abstract":"<div><p>For a differential form on a manifold, having constant components in suitable local coordinates trivially implies being parallel relative to a torsion-free connection, and the converse implication is known to be true for <i>p</i>-forms in dimension <i>n</i> when <span>(p=0,1,2,n-1,n)</span>. We prove the converse for <span>((n-2))</span>-forms, and for 3-forms when <span>(n=6)</span>, while pointing out that it fails to hold for Cartan 3-forms on all simple Lie groups of dimensions <span>(nge 8)</span> as well as for <span>((n,p)=(7,3))</span> and <span>((n,p)=(8,4))</span>, where the 3-forms and 4-forms arise in compact simply connected Riemannian manifolds with exceptional holonomy groups. We also provide geometric characterizations of 3-forms in dimension six and <span>((n-2))</span>-forms in dimension <i>n</i> having the constant-components property mentioned above, and describe examples illustrating the fact that various parts of these geometric characterizations are logically independent.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"69 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-026-10040-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147737756","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Complex structures of the Gibbons-Hawking ansatz with infinite topological type","authors":"Wenxin He,&nbsp;Bin Xu","doi":"10.1007/s10455-026-10039-2","DOIUrl":"10.1007/s10455-026-10039-2","url":null,"abstract":"<div><p>In this paper, we study the complex structures of complete hyperkähler four-manifolds of infinite topological type arising from the Gibbons-Hawking ansatz. We show that for almost all complex structures in the hyperkähler family, the manifold is biholomorphic to a hypersurface in <span>(mathbb {C}^3)</span> defined by an explicit entire function. For the remaining complex structures, we further prove that the manifold is biholomorphic to the minimal resolution of a singular surface in <span>(mathbb {C}^3)</span> under certain conditions. Thus, we partially extend LeBrun’s celebrated work [LeBrun, C.: Complete Ricci-flat Kähler metrics on <span>(mathbb {C} ^n)</span> need not be flat. In Proc. Symp. Pure Math <b>52</b>, 297–304 (1991)] to the context of countably many punctures.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"69 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147737786","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":"Invariants of stably trivial vector bundles with connection","authors":"Sergiu Moroianu","doi":"10.1007/s10455-026-10041-8","DOIUrl":"10.1007/s10455-026-10041-8","url":null,"abstract":"<div><p>We define a Chern–Simons invariant of connections on stably trivial vector bundles over smooth manifolds, taking values in 3-forms modulo closed forms with integral cohomology class. We show an additivity property of this invariant for connections defined on a direct sum of bundles, under a certain block-diagonality condition on the curvature. As a corollary, we deduce an obstruction for conformally immersing a <i>n</i>-dimensional Riemannian manifold in a translation manifold of dimension <span>(n+1)</span>.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"69 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147642361","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 splittings of deformations of pairs of complex structures and holomorphic vector bundles","authors":"Hisashi Kasuya,&nbsp;Valto Purho","doi":"10.1007/s10455-026-10036-5","DOIUrl":"10.1007/s10455-026-10036-5","url":null,"abstract":"<div><p>We can show that the Kuranishi space of a pair (<i>M</i>, <i>E</i>) of a compact Kähler manifold <i>M</i> and its flat Hermitian vector bundle <i>E</i> is isomorphic to the direct product of the Kuranishi space of <i>M</i> and the Kuranishi space of <i>E</i>. We study non-Kähler case. We show that the Kuranishi space of a pair (<i>M</i>, <i>E</i>) of a complex parallelizable nilmanifold <i>M</i> and its trivial holomorphic vector bundle <i>E</i> is isomorphic to the direct product of the Kuranishi space of <i>M</i> and the Kuranishi space of <i>E</i>. We give examples of pairs (<i>M</i>, <i>E</i>) of nilmanifolds <i>M</i> with left-invariant abelian complex structures and their trivial holomorphic line bundles <i>E</i> such that the Kuranishi spaces of pairs (<i>M</i>, <i>E</i>) are not isomorphic to direct products of the Kuranishi spaces of <i>M</i> and the Kuranishi spaces of <i>E</i>.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"69 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147588386","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":"The parallel transport map over reductive homogeneous space","authors":"Masahiro Morimoto","doi":"10.1007/s10455-026-10038-3","DOIUrl":"10.1007/s10455-026-10038-3","url":null,"abstract":"<div><p>We show that the parallel transport map over a reductive homogeneous space with natural torsion-free connection becomes an affine submersion with horizontal distribution. This generalizes one of the main results in the author’s previous paper in the case of affine symmetric spaces. We also prove the compactness of the shape operators of the submanifold lifted by the parallel transport map. This improves a previous result by the author and generalizes some results of Terng-Thorbergsson and of Koike. Furthermore we propose two definitions for the regularized mean curvatures of affine Fredholm submanifolds in Hilbertable spaces and discuss their relations to the parallel transport map. In particular, each fiber of the parallel transport map over a reductive homogeneous space is shown to be minimal in both senses.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"69 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-026-10038-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147607404","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quantization of the Kähler-Ricci flow and optimal destabilizer for a Fano manifold","authors":"Tomoyuki Hisamoto","doi":"10.1007/s10455-025-10025-0","DOIUrl":"10.1007/s10455-025-10025-0","url":null,"abstract":"<div><p>For a Fano manifold, We consider the geometric quantization of the Kähler-Ricci flow and the associated entropy functional. Convergence to the original flow and entropy is established. Based on these results we formulate the finite-dimensional approximation of the optimal degeneration for the anti-canonical polarization.</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"69 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147560241","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}