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Chen Inequalities for Spacelike Submanifolds in Statistical Manifolds of Type Para-Kähler Space Forms

Author

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  • Simona Decu

    (Department of Applied Mathematics, Bucharest University of Economic Studies, 6 Piaţa Romană, 010374 Bucharest, Romania
    Romanian Academy, Costin C. Kiriţescu National Institute of Economic Research—Centre of Mountain Economy (CE-MONT), 13 Calea 13 Septembrie, 030508 Bucharest, Romania
    These authors contributed equally to this work.)

  • Stefan Haesen

    (Department of Mathematics, University of Hasselt, BE 3590 Diepenbeek, Belgium
    Department of Teacher Education, Thomas More University College, 2290 Vorselaar, Belgium
    These authors contributed equally to this work.)

Abstract

In this paper, we prove some inequalities between intrinsic and extrinsic curvature invariants, namely involving the Chen first invariant and the mean curvature of totally real and holomorphic spacelike submanifolds in statistical manifolds of type para-Kähler space forms. Furthermore, we investigate the equality cases of these inequalities. As illustrations of the applications of the above inequalities, we consider a few examples.

Suggested Citation

  • Simona Decu & Stefan Haesen, 2022. "Chen Inequalities for Spacelike Submanifolds in Statistical Manifolds of Type Para-Kähler Space Forms," Mathematics, MDPI, vol. 10(3), pages 1-12, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:3:p:330-:d:730567
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    References listed on IDEAS

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    1. Simona Decu & Stefan Haesen & Leopold Verstraelen, 2020. "Inequalities for the Casorati Curvature of Statistical Manifolds in Holomorphic Statistical Manifolds of Constant Holomorphic Curvature," Mathematics, MDPI, vol. 8(2), pages 1-13, February.
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    Cited by:

    1. Simona Decu, 2022. "Casorati Inequalities for Spacelike Submanifolds in Sasaki-like Statistical Manifolds with Semi-Symmetric Metric Connection," Mathematics, MDPI, vol. 10(19), pages 1-15, September.

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