Equigeodesics on some classes of homogeneous spaces

TL;DR

This paper investigates equigeodesics, which are homogeneous curves that are geodesics under any G-invariant metric, on specific classes of reductive homogeneous spaces including Stiefel manifolds, Wallach spaces, and spheres.

Contribution

It provides a characterization of algebraic equigeodesics on various homogeneous spaces, expanding understanding of their geometric properties.

Findings

Characterization of algebraic equigeodesics on V2Rn and V4R6

Identification of equigeodesics on SO(6) and related spaces

Analysis of equigeodesics on spheres with specific homogeneous structures

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).