Elasticity and conformal tension via the Kaluza-Klein mechanism
type: Item
instance of: scholarly article
title: Elasticity and conformal tension via the Kaluza-Klein mechanism
zbMATH Open document ID: 0993.53021
DOI: 10.1016/S0393-0440(99)00057-1
author: N. Delaunay
published in: Journal of Geometry and Physics
publication date: 2000-11-22T00:00:00Z
review text: The authors consider semi-Riemannian tubes, i.e. warped products \(M\times_f S^1\), where \((M,g)\) is a semi-Riemannian manifold and \(f\) a smooth positive warping function on \(M\). For any \(p\in M\), the fibre \(\gamma_p=\{p\}\times S^1\) provides a circle. The \(r\)-elasticity of fibres is characterized. In particular, a theorem of classification of the triples \((M,g,f)\) which provide a foliation by \(r\)-elastic circles in \(M\times_f S^1\) is proved. Interesting examples are given. For instance, examples of foliated Kaluza-Klein conformal universes with \(G\)-submanifolds leaves are obtained. Among other applications, we mention a characterization of the photon sphere in a Schwarzschild space-time from the point of view of the \(r\)-elasticity.
reviewed by: Ion Mihai
Mathematics Subject Classification ID: 53C50
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 58E50
Mathematics Subject Classification ID: 58E15
Mathematics Subject Classification ID: 83C99
Mathematics Subject Classification ID: 83E50
Mathematics Subject Classification ID: 53C80
zbMATH DE Number: 1491092
zbMATH Keywords: Wilmore-Chen submanifold
zbMATH Keywords: Kaluza-Klein metric
zbMATH Keywords: conformal structure
zbMATH Keywords: warped product
zbMATH Keywords: conformal total tension functional
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1491092