Abstract
Statistical manifolds are abstract generalizations of statistical models introduced by Amari [1] in 1985. Such manifolds have been studied in terms of information geometry which includes the notion of dual connections, called conjugate connection in affine geometry. Recently, Furuhata [5] defined and studied the properties of holomorphic statistical space forms.
In this paper, we obtain the generalized Wintgen type inequality for Lagrangian submanifolds in holomorphic statistical space forms. We also obtain condition under which the submanifold becomes minimal or H is some scalar multiple of \(H^{*}\).
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Nguiffo Boyom, M., Aquib, M., Shahid, M.H., Jamali, M. (2017). Generalized Wintegen Type Inequality for Lagrangian Submanifolds in Holomorphic Statistical Space Forms. 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_19
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DOI: https://doi.org/10.1007/978-3-319-68445-1_19
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