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Surfaces of three-dimensional homogeneous plane waves 三维均匀平面波的表面
IF 1.2 3区 数学
Journal of Geometry and Physics Pub Date : 2025-07-25 DOI: 10.1016/j.geomphys.2025.105603
Giovanni Calvaruso, Lorenzo Pellegrino
{"title":"Surfaces of three-dimensional homogeneous plane waves","authors":"Giovanni Calvaruso,&nbsp;Lorenzo Pellegrino","doi":"10.1016/j.geomphys.2025.105603","DOIUrl":"10.1016/j.geomphys.2025.105603","url":null,"abstract":"<div><div>We investigate the geometry of surfaces in three-dimensional homogeneous non-symmetric plane waves. In particular, we obtain the full classification and explicit description of their totally geodesic and parallel examples and prove the nonexistence of proper totally umbilical surfaces. Moreover, we characterize their minimal surfaces, providing some explicit examples.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"217 ","pages":"Article 105603"},"PeriodicalIF":1.2,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144738584","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}
引用次数: 0
Kähler toric manifolds from dually flat spaces Kähler对偶平坦空间中的环流形
IF 1.2 3区 数学
Journal of Geometry and Physics Pub Date : 2025-07-25 DOI: 10.1016/j.geomphys.2025.105602
Mathieu Molitor
{"title":"Kähler toric manifolds from dually flat spaces","authors":"Mathieu Molitor","doi":"10.1016/j.geomphys.2025.105602","DOIUrl":"10.1016/j.geomphys.2025.105602","url":null,"abstract":"<div><div>We present a novel geometric construction, called <em>torification</em>, that associates Kähler manifolds with torus actions to dually flat manifolds. The construction relies on information-theoretical concepts and aims to provide clear directions for developing Geometric Quantum Mechanics further in finite dimension.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"217 ","pages":"Article 105602"},"PeriodicalIF":1.2,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144738583","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}
引用次数: 0
Rota-Baxter operators on crossed modules of Lie groups and categorical solutions of the Yang-Baxter equation 李群交叉模上的Rota-Baxter算子及Yang-Baxter方程的范畴解
IF 1.2 3区 数学
Journal of Geometry and Physics Pub Date : 2025-07-23 DOI: 10.1016/j.geomphys.2025.105601
Jun Jiang
{"title":"Rota-Baxter operators on crossed modules of Lie groups and categorical solutions of the Yang-Baxter equation","authors":"Jun Jiang","doi":"10.1016/j.geomphys.2025.105601","DOIUrl":"10.1016/j.geomphys.2025.105601","url":null,"abstract":"<div><div>In this paper, we construct a categorical solution <span><math><mo>(</mo><mi>C</mi><mo>,</mo><mi>R</mi><mo>)</mo></math></span> of the Yang-Baxter equation, i.e. <span><math><mi>C</mi></math></span> is a small category and <span><math><mi>R</mi><mo>:</mo><mi>C</mi><mo>×</mo><mi>C</mi><mspace></mspace><mo>→</mo><mspace></mspace><mi>C</mi><mo>×</mo><mi>C</mi></math></span> is an invertible functor satisfying<span><span><span><math><mo>(</mo><mi>R</mi><mo>×</mo><msub><mrow><mi>Id</mi></mrow><mrow><mi>C</mi></mrow></msub><mo>)</mo><mo>(</mo><msub><mrow><mi>Id</mi></mrow><mrow><mi>C</mi></mrow></msub><mo>×</mo><mi>R</mi><mo>)</mo><mo>(</mo><mi>R</mi><mo>×</mo><msub><mrow><mi>Id</mi></mrow><mrow><mi>C</mi></mrow></msub><mo>)</mo><mo>=</mo><mo>(</mo><msub><mrow><mi>Id</mi></mrow><mrow><mi>C</mi></mrow></msub><mo>×</mo><mi>R</mi><mo>)</mo><mo>(</mo><mi>R</mi><mo>×</mo><msub><mrow><mi>Id</mi></mrow><mrow><mi>C</mi></mrow></msub><mo>)</mo><mo>(</mo><msub><mrow><mi>Id</mi></mrow><mrow><mi>C</mi></mrow></msub><mo>×</mo><mi>R</mi><mo>)</mo><mo>,</mo></math></span></span></span> where <span><math><mi>C</mi><mo>×</mo><mi>C</mi></math></span> is the product category. First, the notion of Rota-Baxter operators on crossed modules of Lie groups is defined and its various properties are established. Then, we use Rota-Baxter operators on crossed modules of Lie groups to construct categorical solutions of the Yang-Baxter equation. We also study the Rota-Baxter operators on crossed modules of Lie algebras which are infinitesimals of Rota-Baxter operators on crossed modules of Lie groups, they can give connections on manifolds. Finally, we study the integration of Rota-Baxter operators on crossed modules of Lie algebras and the differentials of Rota-Baxter operators on crossed modules of Lie groups.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"217 ","pages":"Article 105601"},"PeriodicalIF":1.2,"publicationDate":"2025-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144723768","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}
引用次数: 0
Equivalence between Jacobi-orthogonality and Osserman condition in dimension four 四维中jacobi正交与Osserman条件的等价性
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2025-07-22 DOI: 10.1016/j.geomphys.2025.105599
Vladica Andrejić
{"title":"Equivalence between Jacobi-orthogonality and Osserman condition in dimension four","authors":"Vladica Andrejić","doi":"10.1016/j.geomphys.2025.105599","DOIUrl":"10.1016/j.geomphys.2025.105599","url":null,"abstract":"<div><div>An algebraic curvature tensor on a (possibly indefinite) scalar product space is said to be Jacobi-orthogonal if, for any mutually orthogonal vectors <em>X</em> and <em>Y</em>, the Jacobi operator of <em>X</em> applied to <em>Y</em> is orthogonal to the Jacobi operator of <em>Y</em> applied to <em>X</em>. We prove that any four-dimensional algebraic curvature tensor is Jacobi-orthogonal if and only if it is Osserman.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"216 ","pages":"Article 105599"},"PeriodicalIF":1.6,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144695264","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}
引用次数: 0
Indecomposability of derived categories in families 科中派生类的不可分解性
IF 1.2 3区 数学
Journal of Geometry and Physics Pub Date : 2025-07-22 DOI: 10.1016/j.geomphys.2025.105600
Francesco Bastianelli , Pieter Belmans , Shinnosuke Okawa , Andrea T. Ricolfi
{"title":"Indecomposability of derived categories in families","authors":"Francesco Bastianelli ,&nbsp;Pieter Belmans ,&nbsp;Shinnosuke Okawa ,&nbsp;Andrea T. Ricolfi","doi":"10.1016/j.geomphys.2025.105600","DOIUrl":"10.1016/j.geomphys.2025.105600","url":null,"abstract":"<div><div>Using the moduli space of semiorthogonal decompositions in a smooth projective family, introduced by the second, the third and the fourth author, we propose a novel approach to indecomposability questions for derived categories. Modulo a natural conjecture on the structure of the moduli space, we give both general results, and discuss interesting explicit examples of the behaviour of indecomposability in families, by relating it to the behaviour of the canonical base locus in families. These examples are symmetric powers of curves, certain regular surfaces of general type with large canonical base locus, and Hilbert schemes of points on surfaces. Indecomposability for symmetric powers of curves has been settled via other means, the other cases remain open and we expect that our analysis of the base locus will prove instrumental in finding unconditional proofs.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"217 ","pages":"Article 105600"},"PeriodicalIF":1.2,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144723769","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}
引用次数: 0
On entropy and complexity of coherent states and Kähler geometry 论相干态的熵和复杂性与Kähler几何
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2025-07-22 DOI: 10.1016/j.geomphys.2025.105598
Koushik Ray
{"title":"On entropy and complexity of coherent states and Kähler geometry","authors":"Koushik Ray","doi":"10.1016/j.geomphys.2025.105598","DOIUrl":"10.1016/j.geomphys.2025.105598","url":null,"abstract":"<div><div>Consanguinity of entropy and complexity is pointed out through the example of coherent states of the group <span><math><mi>S</mi><mi>L</mi><mo>(</mo><mi>d</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>C</mi><mo>)</mo></math></span>. Both are obtained from the Kähler potential of the underlying geometry of the sphere corresponding to the Fubini-Study metric. Entropy is shown to be equal to the Kähler potential written in terms of dual symplectic variables as the Guillemin potential for toric manifolds. The logarithm of complexity relating two states is shown to be equal to Calabi's diastasis function. Optimality of the Fubini-Study metric is indicated by considering its deformation.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"217 ","pages":"Article 105598"},"PeriodicalIF":1.6,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144714293","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}
引用次数: 0
Polynomial and non-polynomial first integrals of projective structures and geodesic flows 投影结构和测地线流动的多项式和非多项式第一积分
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2025-07-18 DOI: 10.1016/j.geomphys.2025.105596
Maria V. Demina , Anna R. Ishchenko
{"title":"Polynomial and non-polynomial first integrals of projective structures and geodesic flows","authors":"Maria V. Demina ,&nbsp;Anna R. Ishchenko","doi":"10.1016/j.geomphys.2025.105596","DOIUrl":"10.1016/j.geomphys.2025.105596","url":null,"abstract":"<div><div>We develop a method based on the Darboux theory of integrability that is able to produce first integrals of geodesic equations on 2-surfaces. We present local explicit examples of two-dimensional metrics with polynomial in momenta first integrals of arbitrary degrees. We also find metrics admitting transcendental first integrals. In particular, we express some first integrals via the hypergeometric function. Our metrics are parameterized by an arbitrary function of one variable.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"216 ","pages":"Article 105596"},"PeriodicalIF":1.6,"publicationDate":"2025-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144686656","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}
引用次数: 0
Satake's good basic invariants for finite complex reflection groups 有限复反射群的Satake良好的基本不变量
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2025-07-18 DOI: 10.1016/j.geomphys.2025.105597
Yukiko Konishi , Satoshi Minabe
{"title":"Satake's good basic invariants for finite complex reflection groups","authors":"Yukiko Konishi ,&nbsp;Satoshi Minabe","doi":"10.1016/j.geomphys.2025.105597","DOIUrl":"10.1016/j.geomphys.2025.105597","url":null,"abstract":"<div><div>In <span><span>[17]</span></span> Satake introduced the notions of admissible triplets and good basic invariants for finite complex reflection groups. For irreducible finite Coxeter groups, he showed the existence and the uniqueness of good basic invariants. Moreover he showed that good basic invariants are flat in the sense of K. Saito's flat structure. He also obtained a formula for the multiplication of the Frobenius structure. In this article, we generalize his results to finite complex reflection groups. We first study the existence and the uniqueness of good basic invariants. Then for duality groups, we show that good basic invariants are flat in the sense of the natural Saito structure constructed in <span><span>[7]</span></span>. We also give a formula for the potential vector fields of the multiplication in terms of the good basic invariants. Moreover, in the case of irreducible finite Coxeter groups, we derive a formula for the potential functions of the associated Frobenius manifolds.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"216 ","pages":"Article 105597"},"PeriodicalIF":1.6,"publicationDate":"2025-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144686654","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}
引用次数: 0
An elliptic fibration arising from the Lagrange top and its monodromy 由拉格朗日顶及其单一性引起的椭圆型颤动
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2025-07-17 DOI: 10.1016/j.geomphys.2025.105595
Genki Ishikawa
{"title":"An elliptic fibration arising from the Lagrange top and its monodromy","authors":"Genki Ishikawa","doi":"10.1016/j.geomphys.2025.105595","DOIUrl":"10.1016/j.geomphys.2025.105595","url":null,"abstract":"<div><div>This paper is to investigate an elliptic fibration over <span><math><mi>C</mi><msup><mrow><mi>P</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> arising from the Lagrange top from the viewpoint of complex algebraic geometry. The description of the discriminant locus of this elliptic fibration is given in detail. Moreover, the concrete description of the discriminant locus and the complete classification of singular fibres of the elliptic fibration are obtained according to Miranda's theory of elliptic threefolds after suitable modifications of the base and total spaces. Furthermore, the monodromy of the elliptic fibration is described.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"216 ","pages":"Article 105595"},"PeriodicalIF":1.6,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144686655","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}
引用次数: 0
On the geometry of compatible Poisson and Riemannian structures 相容泊松和黎曼结构的几何
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2025-07-16 DOI: 10.1016/j.geomphys.2025.105593
Nicolás Martínez Alba , Andrés Vargas
{"title":"On the geometry of compatible Poisson and Riemannian structures","authors":"Nicolás Martínez Alba ,&nbsp;Andrés Vargas","doi":"10.1016/j.geomphys.2025.105593","DOIUrl":"10.1016/j.geomphys.2025.105593","url":null,"abstract":"<div><div>We consider compatibility conditions between Poisson and Riemannian structures on smooth manifolds by means of a contravariant Levi-Civita connection. These include Riemann–Poisson structures (as defined by M. Boucetta), and the class of almost Kähler–Poisson manifolds, introduced with the aid of a contravariant <em>f</em>-structure, that will be called <em>partially co-complex structure</em>, in analogy with complex ones on Kähler manifolds. Additionally, we study the geometry of the symplectic foliation, and the behavior of these compatibilities under structure preserving maps and symmetries.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"216 ","pages":"Article 105593"},"PeriodicalIF":1.6,"publicationDate":"2025-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144679593","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}
引用次数: 0
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