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

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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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  1. Majid Ali Choudhary

    Present address: Department of Mathematics, School of Sciences, Maulana Azad National Urdu University, Hyderabad, India

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  1. Department of Mathematics, Zakir Husain Delhi College(Evening), New Delhi, 110002, India

    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. 32, 725–732 (2021). https://doi.org/10.1007/s13370-020-00856-4

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