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).