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 ∇∗.
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© 2014 Springer International Publishing Switzerland
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Calin, O., Udrişte, C. (2014). Dual Laplacians. In: Geometric Modeling in Probability and Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-07779-6_10
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DOI: https://doi.org/10.1007/978-3-319-07779-6_10
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-07778-9
Online ISBN: 978-3-319-07779-6
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