首页|The symmetric space,strong isotropy irreducibility and equigeodesic properties

The symmetric space,strong isotropy irreducibility and equigeodesic properties

扫码查看
原文链接
  • 万方数据
  • 维普
A smooth curve on a homogeneous manifold G/H is called a Riemannian equigeodesic if it is a homogeneous geodesic for any G-invariant Riemannian metric.The homogeneous manifold G/H is called Riemannian equigeodesic,if for any x ∈ G/H and any nonzero y ∈ Tx(G/H),there exists a Riemannian equigeodesic c(t)with c(0)=x and (c)(0)=y.These two notions can be naturally transferred to the Finsler setting,which provides the definitions for Finsler equigeodesics and Finsler equigeodesic spaces.We prove two classification theorems for Riemannian equigeodesic spaces and Finsler equigeodesic spaces,respectively.Firstly,a homogeneous manifold G/H with a connected simply connected quasi compact G and a connected H is Riemannian equigeodesic if and only if it can be decomposed as a product of Euclidean factors and compact strongly isotropy irreducible factors.Secondly,a homogeneous manifold G/H with a compact semisimple G is Finsler equigeodesic if and only if it can be locally decomposed as a product,in which each factor is Spin(7)/G2,G2/SU(3) or a symmetric space of compact type.These results imply that the symmetric space and the strongly isotropy irreducible space of compact type can be interpreted by equigeodesic properties.As an application,we classify the homogeneous manifold G/H with a compact semisimple G such that all the G-invariant Finsler metrics on G/H are Berwald.It suggests a new project in homogeneous Finsler geometry,i.e.,to systematically study the homogeneous manifold G/H on which all the G-invariant Finsler metrics satisfy a certain geometric property.

equigeodesicequigeodesic spaceflag manifoldorbit type stratificationsymmetric spacestrongly isotropy irreducible space

Ming Xu、Ju Tan

展开 >

School of Mathematical Sciences,Capital Normal University,Beijing 100048,China

School of Microelectronics and Data Science,Anhui University of Technology,Ma'anshan 243032,China

National Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaBeijing Natural Science FoundationNatural Science Foundation of Anhui Province

12131012120010071182110112220031908085QA03

2024

10.1007/s11425-022-2090-1

中国科学:数学(英文版)
中国科学院

中国科学:数学(英文版)

CSTPCD
影响因子：0.36
ISSN：1674-7283
年,卷(期)：2024.67(1)
  • 47