Statistical Submanifolds

Ovidiu Calin and Constantin Udrişte
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Ovidiu Calin: Eastern Michigan University, Department of Mathematics
Constantin Udrişte: University Politehnica of Bucharest, Faculty of Applied Sciences Department of Mathematics-Informatics

Chapter Chapter 13 in Geometric Modeling in Probability and Statistics, 2014, pp 335-355 from Springer

Abstract: Abstract This chapter studies the geometric structure induced on a submanifold by the dualistic structure of a statistical manifold. This includes the study of the first and second fundamental forms, curvatures, mean curvatures, and the relations among them. This material adapts the well-known theory of submanifolds to the statistical manifolds framework and consists mainly in the contributions of the authors.

Keywords: Vector Field; Fundamental Form; Curvature Tensor; Exponential Family; Shape Operator (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-07779-6_13

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DOI: 10.1007/978-3-319-07779-6_13

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