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On 2-Stein Submanifolds in Space Forms

Abstract

We prove that a 2-stein submanifold in a space form whose normal connection is flat or whose codimension is at most 2, has constant curvature.

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Acknowledgements

The authors are thankful to the referee for useful suggestions.

Funding

The first and the fourth author were supported by Samsung Science and Technology Foundation under Project No. SSTF-BA2001-03. The third author was partially supported by the ARC (Australian Research Council) Discovery Grant DP210100951.

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Correspondence to JeongHyeong Park.

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Euh, Y., Kim, J., Nikolayevsky, Y. et al. On 2-Stein Submanifolds in Space Forms. Results Math 77, 84 (2022). https://doi.org/10.1007/s00025-022-01620-9

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  • DOI: https://doi.org/10.1007/s00025-022-01620-9

Keywords

  • 2-stein space
  • submanifold in a space form

Mathematics Subject Classification

  • Primary 53C25
  • 53B25