Dual Volume Elements

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 9 in Geometric Modeling in Probability and Statistics, 2014, pp 257-290 from Springer

Abstract: Abstract This chapter defines the volume elements associated with two dual connections and investigates their relationship. First, we define the Riemannian volume element and show that it is parallel with respect to the Levi–Civita connection. Since the converse is also true, this provides an alternate definition for the volume element used in defining volume elements associated with other connections. In particular, we define and study the volume element associated with an α-connection. The volume elements for the exponential model and mixture model are computed, as examples of distinguished importance in the theory.

Keywords: Vector Field; Mixture Model; Volume Element; Constant Curvature; Integral Curve (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_9

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DOI: 10.1007/978-3-319-07779-6_9

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