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Inequalities for the Casorati Curvature of Statistical Manifolds in Holomorphic Statistical Manifolds of Constant Holomorphic Curvature

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.)

  • Leopold Verstraelen

    (Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, Box 2400, BE-3001 Leuven, Belgium
    These authors contributed equally to this work.)

Abstract

In this paper, we prove some inequalities in terms of the normalized δ -Casorati curvatures (extrinsic invariants) and the scalar curvature (intrinsic invariant) of statistical submanifolds in holomorphic statistical manifolds with constant holomorphic sectional curvature. Moreover, we study the equality cases of such inequalities. An example on these submanifolds is presented.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:251-:d:320685
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    Cited by:

    1. 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.

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