On some differential operators on natural Riemann extensions

Natural Riemann extensions are pseudo-Riemannian metrics (introduced by Sekizawa and studied then by Kowalski–Sekizawa), which generalize the classical Riemann extension defined by Patterson–Walker. Let M be a manifold with an affine connection and let T ∗ M be the total space of its cotangent bundl...

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Bibliographic Details
Published inAnnals of global analysis and geometry Vol. 48; no. 2; pp. 171 - 180
Main Authors Bejan, Cornelia-Livia, Kowalski, Oldřich
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.08.2015
Springer Nature B.V
Subjects
Analysis
Bundling
Differential Geometry
Geometry
Global Analysis and Analysis on Manifolds
Laplace transforms
Manifolds (mathematics)
Mathematical analysis
Mathematical Physics
Mathematics
Mathematics and Statistics
Operators
Studies
Texts
Topological manifolds
Natural Riemann extension
53C50
58E20
Cotangent bundle
53C43
53B05
Riemannian manifold
Harmonic function
Laplacian operator
53C07
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Summary:Natural Riemann extensions are pseudo-Riemannian metrics (introduced by Sekizawa and studied then by Kowalski–Sekizawa), which generalize the classical Riemann extension defined by Patterson–Walker. Let M be a manifold with an affine connection and let T ∗ M be the total space of its cotangent bundle. On T ∗ M endowed with a natural Riemann extension, we study here the Laplacian and give necessary and sufficient conditions for the harmonicity of a certain family of (local) functions. We also prove a gradient formula for natural Riemann extensions.
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ISSN:0232-704X
1572-9060
DOI:10.1007/s10455-015-9463-3