Dual Laplacians

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 10 in Geometric Modeling in Probability and Statistics, 2014, pp 291-302 from Springer

Abstract: Abstract Each linear connection induces a divergence, which is used to define a Laplacian. Dual connections yield to dual Laplacians. This chapter deals with the definition and main properties of dual Laplacians and α-Laplacians. Their relationship with Hessians, curvature vector fields, and dual volume elements is emphasized. In this chapter (M, g, ∇, ∇∗) is a manifold M structured by a metric g, and endowed with a pair of dual connections ∇ and ∇∗.

Keywords: Vector Field; Riemannian Manifold; Volume Element; Dual Divergence; Exponential Family (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_10

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DOI: 10.1007/978-3-319-07779-6_10

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