Isometric immersions with singularities between space forms of the same positive curvature

Abstract

In this paper, we give a definition of coherent tangent bundles of space form type, which is a generalized notion of space forms. Then, we classify their realizations in the sphere as a wave front, which is a generalization of a theorem of O'Neill and Stiel: any isometric immersion of the n-sphere into the (n+1)-sphere of the same sectional curvature is totally geodesic.

16 pages, 11 figures

References in corpus (1)

• An index formula for a bundle homomorphism of the tangent bundle into a vector bundle of the same rank, and its applications