Equigeodesic vectors on compact homogeneous spaces with equivalent isotropy summands

In this paper, we investigate equigeodesics on a compact homogeneous space \(M=G/H.\) $M=G/H.$ 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.