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Sequential warped product submanifolds having holomorphic, totally real and pointwise slant factors

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Abstract

We introduce sequential warped product submanifolds of Kaehler manifolds, provide examples and establish Chen’s inequality for such submanifolds. The equality case is also studied. Moreover, inspired by Lawson and Simons’s integral currrent’s theorem on a submanifold, we find a similar pinching inequality for a sequential warped product submanifold and obtain geometric results when the equality case is satisfied.

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Acknowledgements

The author is grateful to the referees for their valuable comments and suggestions.

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  1. Department of Mathematics, Ege University, 35100, Izmir, Turkey

    Bayram Şahin

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  1. Bayram Şahin
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Correspondence to Bayram Şahin.

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This work is dedicated to the memory of Professor Aurel Bejancu (1946–2020).

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Şahin, B. Sequential warped product submanifolds having holomorphic, totally real and pointwise slant factors. Period Math Hung 85, 128–139 (2022). https://doi.org/10.1007/s10998-021-00422-w

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