Isometric immersions with singularities between space forms of the same positive curvature
Differential Geometry
2015-08-31 v1
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.
Keywords
Cite
@article{arxiv.1508.07223,
title = {Isometric immersions with singularities between space forms of the same positive curvature},
author = {Atsufumi Honda},
journal= {arXiv preprint arXiv:1508.07223},
year = {2015}
}
Comments
16 pages, 11 figures