关于同质性的一个与G2有关的超极性作用

IF 0.7 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications Pub Date : 2025-07-15 DOI:10.1016/j.difgeo.2025.102271

Shinji Ohno , Yuuki Sasaki

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引用次数: 0

摘要

将紧型不可约黎曼对称空间上的同质性一作用分为三种情况：Hermann作用、由2阶黎曼对称空间的线性各向同性表示诱导的作用和例外作用。本文考虑了与异常紧李群G2相关的异常作用，并研究了它们的轨道作为黎曼子流形的一些性质。特别地，我们研究了主轨道的主曲率，并对最小、严格、弱反射和固有双调和的主轨道进行了分类。

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On cohomogeneity one hyperpolar actions related to G2

Cohomogeneity one actions on irreducible Riemannian symmetric spaces of compact type are classified into three cases: Hermann actions, actions induced by the linear isotropy representation of a Riemannian symmetric space of rank 2, and exceptional actions. In this paper, we consider exceptional actions related to the exceptional compact Lie group

G_{2}

and investigate some properties of their orbits as Riemannian submanifolds. In particular, we examine the principal curvatures of principal orbits and classify principal orbits that are minimal, austere, weakly reflective, and proper biharmonic.

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来源期刊

Differential Geometry and its Applications 数学-数学

CiteScore

1.00

自引率

20.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Differential Geometry and its Applications publishes original research papers and survey papers in differential geometry and in all interdisciplinary areas in mathematics which use differential geometric methods and investigate geometrical structures. The following main areas are covered: differential equations on manifolds, global analysis, Lie groups, local and global differential geometry, the calculus of variations on manifolds, topology of manifolds, and mathematical physics.