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

Autor:	Stefan Haesen, Simona Decu, Leopold Verstraelen
Rok vydání:	2020
Předmět:	Pure mathematics General Mathematics Holomorphic function 02 engineering and technology Curvature 01 natural sciences CLASSIFICATION TERMS 0202 electrical engineering electronic engineering information engineering Computer Science (miscellaneous) COMPLEX-SPACE-FORMS Sectional curvature 0101 mathematics Invariant (mathematics) Mathematics::Symplectic Geometry Engineering (miscellaneous) Mathematics Science & Technology LAGRANGIAN SUBMANIFOLDS GEOMETRY Mathematics::Complex Variables lcsh:Mathematics Casorati curvature 010102 general mathematics lcsh:QA1-939 statistical submanifold holomorphic statistical manifold Physical Sciences Computer Science::Programming Languages casorati curvature 020201 artificial intelligence & image processing Mathematics::Differential Geometry Scalar curvature
Zdroj:	Mathematics, Vol 8, Iss 2, p 251 (2020) Mathematics; Volume 8; Issue 2; Pages: 251 Article
ISSN:	2227-7390
DOI:	10.3390/math8020251
Popis:	In this paper, we prove some inequalities in terms of the normalized delta-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. Decu, S (reprint author), Bucharest Univ Econ Studies, Dept Appl Math, 6 Piata Romana, Bucharest 010374, Romania; Romanian Acad, Costin C Kiritescu Natl Inst Econ Res, Ctr Mt Econ CE MONT, 13 Calea 13 Septembrie, Bucharest 030508, Romania. simona.decu@gmail.com; stefan.haesen@uhasselt.be; leopold.verstraelen@wis.kuleuven.be
Databáze:	OpenAIRE
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