Open AccessSymmetric Spaces in Riemannian and Semi-Riemannian Geometry
Author(s) -
Ehsan Hashempour,
Mir Mohammad Seyedvalilo
Publication year - 2020
Publication title -
asian research journal of mathematics
Language(s) - English
Resource type - Journals
ISSN - 2456-477X
DOI - 10.9734/arjom/2020/v16i430186
Subject(s) - symmetric space , mathematics , fundamental theorem of riemannian geometry , riemannian geometry , pure mathematics , exponential map (riemannian geometry) , riemannian manifold , space (punctuation) , manifold (fluid mechanics) , homogeneous space , sectional curvature , mathematical analysis , scalar curvature , homogeneous , curvature , curvature of riemannian manifolds , lie group , riemannian submersion , pseudo riemannian manifold , geometry , combinatorics , computer science , mechanical engineering , engineering , operating system
In this paper, we will obtain the necessary and sufficient conditions for the analysis of the position of local symmetry on an arbitrary Riemannian manifold. These conditions are devoid of the aspects of Lie groups, and thus can be used in calculations of procedures, without interfering with the concepts of Lie groups, and improve intuitive attitudes. Also, we will study and create equivalent conditions for a situation where a two-metric homogeneous Riemannian manifold is located symmetrically. In addition, in this paper it is stated that the symmetric space (M, g) can be seen as a homogeneous space G/K. Also, one-to-one correspondence between the symmetric space and the symmetric pair is shown, and curvature is studied on a symmetric space.