Equigeodesics on some classes of homogeneous spaces
Differential Geometry
2021-06-04 v1
Abstract
We study homogeneous curves on some classes of reductive homogeneous spaces G=H which are geodesics with respect to any G-invariant metric on G=H. These curves are called equigeodesics. The spaces we consider are certain Stiefel manifolds VkRn, generalized Wallach spaces and spheres. We give a characterization for algebraic equigeodesics on V2Rn, V4R6, SO(6)= SO(3) ? SO(2), W6 = U(3)= U(1)3, W12 = Sp(3)= Sp(1)3, S2n+1 ?= U(n + 1)= U(n) and S4n+3 ?= Sp(n + 1)= Sp(n).
Keywords
Cite
@article{arxiv.2105.09184,
title = {Equigeodesics on some classes of homogeneous spaces},
author = {Marina Statha},
journal= {arXiv preprint arXiv:2105.09184},
year = {2021}
}
Comments
16 pages