# A pinching theorem for statistical manifolds with Casorati curvatures

Volume 10, Issue 9, pp 4908--4914
Publication Date: September 22, 2017 Submission Date: October 05, 2016
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### Authors

Chul Woo Lee - Department of Mathematics, Kyungpook National University, Daegu 41566, South Korea. Dae Won Yoon - Department of Mathematics Education, Gyeongsang National University and RINS, Jinju 52828, South Korea. Jae Won Lee - Department of Mathematics Education, Gyeongsang National University and RINS, Jinju 52828, South Korea.

### Abstract

With a pair of conjugate connections $\overline{\nabla}$ and $\overline{\nabla}^*$, we derive optimal Casorati inequalities with the normalized scalar curvature on submanifolds of a statistical manifold of constant curvature.

### Share and Cite

##### ISRP Style

Chul Woo Lee, Dae Won Yoon, Jae Won Lee, A pinching theorem for statistical manifolds with Casorati curvatures, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 9, 4908--4914

##### AMA Style

Lee Chul Woo, Yoon Dae Won, Lee Jae Won, A pinching theorem for statistical manifolds with Casorati curvatures. J. Nonlinear Sci. Appl. (2017); 10(9):4908--4914

##### Chicago/Turabian Style

Lee, Chul Woo, Yoon, Dae Won, Lee, Jae Won. "A pinching theorem for statistical manifolds with Casorati curvatures." Journal of Nonlinear Sciences and Applications, 10, no. 9 (2017): 4908--4914

### Keywords

• Statistical manifolds
• dual connection
• Casorati curvature
• $\delta$-Casorati curvature
• normalized scalar curvature

•  53C05
•  49K35
•  62B10

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