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Optimal inequalities for Riemannian maps and Riemannian submersions involving Casorati curvatures

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Abstract

Riemannian maps are generalizations of well-known notions of isometric immersions and Riemannian submersions. Most optimal inequalities on submanifolds in various ambient spaces are driven from isometric immersions. The main aim of this paper is to obtain optimal inequalities for Riemannian maps to space forms, as well as for Riemannian submersions from space forms, involving Casorati curvatures.

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Acknowledgements

Chul Woo Lee was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education (2018R1D1A1B07040576). Jae Won Lee was supported under the framework of international cooperation program managed by the National Research Foundation of Korea (2019K2A9A1A06097856), and Bayram Sahin was supported under the framework of international cooperation program managed by the Scientific and Technological Research Council of Turkey with project id: 119N087.

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Authors and Affiliations

  1. Department of Mathematics, Kyungpook National University, Daegu, 41566, South Korea

    Chul Woo Lee

  2. Department of Mathematics Education and RINS, Gyeongsang National University, Jinju, 52828, South Korea

    Jae Won Lee

  3. Department of Mathematics, Ege University, Izmir, Turkey

    Bayram Şahin

  4. Research Center in Geometry, Topology and Algebra, Faculty of Mathematics and Computer Science, University of Bucharest, Str. Academiei, Nr. 14, Sector 1, 70109, Bucureşti, Romania

    Gabriel-Eduard Vîlcu

  5. Department of Cybernetics, Economic Informatics, Finance and Accountancy, Petroleum-Gas University of Ploieşti, Bd. Bucureşti, Nr. 39, 100680, Ploieşti, Romania

    Gabriel-Eduard Vîlcu

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  1. Chul Woo Lee
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  2. Jae Won Lee
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  3. Bayram Şahin
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  4. Gabriel-Eduard Vîlcu
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Correspondence to Jae Won Lee.

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Lee, C.W., Lee, J.W., Şahin, B. et al. Optimal inequalities for Riemannian maps and Riemannian submersions involving Casorati curvatures. Annali di Matematica 200, 1277–1295 (2021). https://doi.org/10.1007/s10231-020-01037-7

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  • DOI: https://doi.org/10.1007/s10231-020-01037-7

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