On pseudo-umbilical spacelike submanifolds in indefinite space form \(\mathcal {M}_p^{n+p}(c)\)

Abstract

An intrinsic condition for Pseudo-umbilical spacelike submanifold immersed in indefinite space form is derived, which is used to show that such submanifold is totally geodesic. Next, using a result of Aiyama (Tokyo J Math 18:81–90, 1995), it is proved that Pseudo-umbilical spacelike submanifold is totally umbilical.

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Acknowledgements

The author was helped financially by DST, Govt. of India (DST/INSPIRE Fellowship/2009/[xxv]).

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Correspondence to Majid Ali Choudhary.

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Choudhary, M.A. On pseudo-umbilical spacelike submanifolds in indefinite space form \(\mathcal {M}_p^{n+p}(c)\). Afr. Mat. (2021). https://doi.org/10.1007/s13370-020-00856-4

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Keywords

  • Pseudo-umbilical submanifold
  • Indefinite space form
  • Space-like hypersurface

Mathematics Subject Classification

  • 53C42
  • 53C40
  • 53C50