Isometric immersion of Riemannian homogeneous manifolds

Abstract

Theorem. Let M be a compact connected Riemannian homogeneous manifold with irreducibleisotropy action. For an equivariant isametric immersion f of M into a Euclidean space EN {considered as a Euclidean vector space) there exist a finite number of vector subspaces Eo, Eu ・■・ , Er of EN, isometric immersions ft of 1-type of M into Et (7=1, ・・・, r), constant vector v0 in Eo and positiveconstant aX)・・・,ar so that (1) EN=E0+E1-{■・■ +Er (Euclidean direct sum) (2) /=yo+fli/i+-+ar/r.