Equigeodesic vectors on compact homogeneous spaces with equivalent isotropy summands

TL;DR

This paper studies equigeodesic vectors on compact homogeneous spaces, providing a new formula based on isotropy representation and Lie algebra structure, with applications to M-spaces.

Contribution

It introduces a novel formula for identifying equigeodesic vectors using isotropy representation and Lie algebra structure, advancing understanding of homogeneous space geometry.

Findings

Derived a formula for equigeodesic vectors based on isotropy representation

Applied the formula to specific M-spaces

Enhanced methods for analyzing geodesics on homogeneous spaces

Abstract

In this paper, we investigate equigeodesics on a compact homogeneous space $M=G/H.$ We introduce a formula for the identification of equigeodesic vectors only relying on the isotropy representation of $M$ and the Lie structure of the Lie algebra of $G$. Applications to $M$-spaces are also discussed.