Isometric immersions of higher codimension into the product ${\mathbf S^k \times H^{n+p-k}}$ of sphere and hyperboloid

Xingxiao Li; Tianqun Zhang

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arXiv · 1311.3849

Isometric immersions of higher codimension into the product ${\mathbf S^k \times H^{n+p-k}}$ of sphere and hyperboloid

Xingxiao Li·Tianqun Zhang

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Abstract

In this paper, we obtain a sufficient and necessary condition for a simply connected Riemannian manifold $(M^n, g)$ to be isometrically immersed, as a submanifold with codimension $p\geq 1$, into the product $S^k\times H^{n+p-k}$ of sphere and hyperboloid.

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Xingxiao Li, Tianqun Zhang. 2013-11-15. Isometric immersions of higher codimension into the product ${\mathbf S^k \times H^{n+p-k}}$ of sphere and hyperboloid. https://arxiv.org/abs/1311.3849

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