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Open AccessArticle

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

by Simona Decu 1,2,*,†, Stefan Haesen 3,4,† and Leopold Verstraelen 5,†
1
Department of Applied Mathematics, Bucharest University of Economic Studies, 6 Piaţa Romană, 010374 Bucharest, Romania
2
Romanian Academy, Costin C. Kiriţescu National Institute of Economic Research—Centre of Mountain Economy (CE-MONT), 13 Calea 13 Septembrie, 030508 Bucharest, Romania
3
Department of Mathematics, University of Hasselt, BE 3590 Diepenbeek, Belgium
4
Department of Teacher Education, Thomas More University College, 2290 Vorselaar, Belgium
5
Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, Box 2400, BE-3001 Leuven, Belgium
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2020, 8(2), 251; https://doi.org/10.3390/math8020251
Received: 16 December 2019 / Revised: 7 February 2020 / Accepted: 9 February 2020 / Published: 14 February 2020
(This article belongs to the Special Issue Inequalities in Geometry and Applications)
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. View Full-Text
Keywords: Casorati curvature; statistical submanifold; holomorphic statistical manifold Casorati curvature; statistical submanifold; holomorphic statistical manifold
MDPI and ACS Style

Decu, S.; Haesen, S.; Verstraelen, L. Inequalities for the Casorati Curvature of Statistical Manifolds in Holomorphic Statistical Manifolds of Constant Holomorphic Curvature. Mathematics 2020, 8, 251.

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