Abstract
In 1985, Amari [1] introduced an interesting manifold, i.e., statistical manifold in the context of information geometry. The geometry of such manifolds includes the notion of dual connections, called conjugate connections in affine geometry, it is closely related to affine geometry. A statistical structure is a generalization of a Hessian one, it connects Hessian geometry.
In the present paper, we study CR-statistical submanifolds in holomorphic statistical manifolds. Some results on totally umbilical CR-statistical submanifolds with respect to \(\overline{\nabla }\) and \(\overline{\nabla }^{*}\) in holomorphic statistical manifolds with constant holomorphic curvature are obtained.
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The authors are grateful to the referee for his/her valuable comments and suggestions.
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Boyom, M.N., Siddiqui, A.N., Othman, W.A.M., Shahid, M.H. (2017). Classification of Totally Umbilical CR-Statistical Submanifolds in Holomorphic Statistical Manifolds with Constant Holomorphic Curvature. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2017. Lecture Notes in Computer Science(), vol 10589. Springer, Cham. https://doi.org/10.1007/978-3-319-68445-1_93
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DOI: https://doi.org/10.1007/978-3-319-68445-1_93
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