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Isometric Immersions into \({\mathbb{S}^m \times \mathbb{R}}\) and \({\mathbb{H}^m \times \mathbb{R}}\) with High Codimensions

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Abstract

In this paper, we obtain sufficient and necessary conditions for a simply connected Riemannian manifold (M n, g) to be isometrically immersed into \({\mathbb{S}^m \times \mathbb{R}}\) and \({\mathbb{H}^m \times \mathbb{R}}\).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China

    Qun Chen & Qing Cui

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  1. Qun Chen
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  2. Qing Cui
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Correspondence to Qing Cui.

Additional information

The research was partially supported by NSFC (grant no. 10871149) and RFDP (grant no. 200804860046).

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Chen, Q., Cui, Q. Isometric Immersions into \({\mathbb{S}^m \times \mathbb{R}}\) and \({\mathbb{H}^m \times \mathbb{R}}\) with High Codimensions. Results. Math. 57, 319–333 (2010). https://doi.org/10.1007/s00025-010-0031-7

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  • DOI: https://doi.org/10.1007/s00025-010-0031-7

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