Naturality of homogeneous metrics on Stiefel manifolds SO(m+1)/SO(m-1)

Abstract

It is well known that the unit tangent sphere bundle T_1SM of the standard sphere S^m can be naturally identified with the Stiefel manifold V_2R^m+1 = SO(m + 1)/SO(m - 1). In this paper, we construct the (1-1) correspondence between all SO(m + 1)-invariant homogeneous metrics on V_2R^m+1 and all so-called g-natural metrics on T_1SM.

Keywords

• Naturality
• homogeneous
• metrics
• Stiefel
• manifolds
• SO(m+1)/SO(m-1)