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

Atsufumi Honda

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arXiv · 1508.07223

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

Atsufumi Honda

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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.

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Atsufumi Honda. 2015-08-28. Isometric immersions with singularities between space forms of the same positive curvature. https://arxiv.org/abs/1508.07223

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