常曲率统计流形中子流形的广义标准δ-Casorati曲率不等式#br#

Abstract

Abstract: We considered submanifolds in statistical manifolds of constant curvatures by using Oprea’s optimization method, and obtained some geometric inequalities involving the generalized normalized δ-Casorati curvatures. We gave the upper bound and the lower bound of the normalized scalar curvature of the submanifolds, respectively, and the properties of submanifolds satisfying the equality cases.

Key words: statistical manifold, submanifold, generalized normalized δ-Casorati curvature, inequality

CLC Number:

O186.11

CAI Dandan, LIU Xudong, ZHANG Liang. Inequalities on Generalized Normalized δ-Casorati Curvatures forSubmanifolds in Statistical Manifolds of Constant Curvatures#br#[J].Journal of Jilin University Science Edition, 2019, 57(2): 206-212.

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Inequalities on Generalized Normalized δ-Casorati Curvatures forSubmanifolds in Statistical Manifolds of Constant Curvatures#br#

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