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Inequalities on Riemannian Warped Product Submersions for Vertical Casorati Curvatures

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Abstract

The first and second authors introduced Riemannian warped product submersions and discussed interesting fundamental geometric properties of such submersions in Küpeli Erken and Murathan, Results Math 76(1) (2021), https://doi.org/10.1007/s00025-020-01310-4. In the present paper, we extend this study to put light on the curvature properties of such submersions and then obtain optimal inequalities for Riemannian warped product submersions involving vertical Casorati curvatures. Also, we discuss under which conditions the equality case of inequality can hold with an example.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Engineering and Natural Sciences, Bursa Technical University, Bursa, Turkey

    Irem Küpeli Erken

  2. Department of Mathematics, Art and Science Faculty, Bursa Uludag University, 16059, Bursa, Turkey

    Cengizhan Murathan

  3. Division of Mathematics, School of Basic and Applied Sciences, Galgotias University, Greater Noida, Uttar Pradesh, 203201, India

    Aliya Naaz Siddiqui

Authors
  1. Irem Küpeli Erken
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  2. Cengizhan Murathan
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  3. Aliya Naaz Siddiqui
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Correspondence to Aliya Naaz Siddiqui.

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Erken, I.K., Murathan, C. & Siddiqui, A.N. Inequalities on Riemannian Warped Product Submersions for Vertical Casorati Curvatures. Mediterr. J. Math. 20, 98 (2023). https://doi.org/10.1007/s00009-023-02313-5

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  • DOI: https://doi.org/10.1007/s00009-023-02313-5

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