Sasakian流形曲率条件的刻画
Characterization of Sasakian Manifolds by Curvature Conditions
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中文总结 AI 辅助
本文利用部分Ricci流，在$(\nkappa,\mu)$-零化条件下刻画了弱接触度量流形中的Sasakian结构，并给出了双Legendre结构的存在条件及分裂分类结果。
中文摘要 AI 辅助
Sasakian流形是接触度量流形的一个子类，在现代微分几何和数学物理中扮演核心角色，它们自然地出现在几何力学、CR几何和超对称场论中。弱接触度量（w.c.m.）结构推广了接触度量结构，为研究接触几何及其应用提供了更广泛的框架。一个基本问题是理解曲率条件如何约束底层接触度量结构，特别是它们如何区分Sasakian几何与其更弱的变体。利用部分Ricci流，我们在与曲率相关的$(\kappa,\mu)$-零化条件下刻画了（在w.c.m.流形中的）Sasakian结构。对于$\kappa<1$，我们找到了w.c.m.流形允许双Legendre结构的条件，并且对于$\kappa=\mu=0$，建立了分裂和分类结果。
英文摘要
Sasakian manifolds, a subclass of contact metric manifolds, play a central role in modern differential geometry and mathematical physics, where they arise naturally in geometric mechanics, CR geometry, and supersymmetric field theories. The weak contact metric (w.c.m.) structure generalizes the contact metric structure and provides a broader framework for studying contact geometry and its applications. A fundamental problem is to understand how curvature conditions constrain the underlying contact metric structure and, in particular, how they distinguish Sasakian geometry from its weaker variants. Using the partial Ricci flow, we characterize Sasakian structure (among w.c.m. manifolds) under the $(κ,μ)$-nullity condition related to curvature. For $κ<1$ we find conditions under which a w.c.m. manifold admits a bi-Legendrian structure, and for $κ=μ=0$ establish splitting and classification results.
发表机构
- Indian Institute of Technology - Hyderabad（印度理工学院海德拉巴分校）
- University of Haifa（海法大学）
机构由 AI 辅助整理，请以论文原文为准。
