Equigeodesics on some classes of homogeneous spaces

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).