\(g\)-natural contact metrics on unit tangent sphere bundles
type: Item
instance of: scholarly article
title: \(g\)-natural contact metrics on unit tangent sphere bundles
zbMATH Open document ID: 1128.53049
author: Giovanni Calvaruso
author: Mohamed Tahar Kadaoui Abbassi
published in: Monatshefte für Mathematik
publication date: 2007-07-19T00:00:00Z
review text: Let \((M^m,g)\) be a Riemannian manifold and \(T_1M\) - its unit tangent sphere bundle. \(T_1M\) is equipped with the standard contact metric structure \((\eta,\widetilde{g})\). In this paper the standard contact metric structure of \(T_1M\) is replaced by a three-parameter family of contact metric structures \((\widetilde{\eta},\widetilde{G})\) whose Riemannian metric \(\widetilde{G}\) are \(g\)-natural. The authors investigate the contact metric properties of \((T_1M, \widetilde{\eta}, \widetilde{G})\) which are reflected by the geometry of the base manifold. The authors obtain necessary and sufficient conditions for a contact metric structure to be \(K\)-contact, Sasakian, to satisfy some variational conditions or to define a strongly pseudo-convex CR-structure. The results obtained generalize classical theorems on the standard contact metric structure on \(T_1M\).
Mathematics Subject Classification ID: 53D10
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 53C25
zbMATH DE Number: 5172603
zbMATH Keywords: unit tangent sphere bundle
zbMATH Keywords: \(g\)-natural metric
zbMATH Keywords: contact metric geometry
reviewed by: Nicolai K. Smolentsev
MaRDI profile type: Publication
full work available at URL: s00605-006-0421-9
OpenAlex ID: W1980844866
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DOI: 10.1007/S00605-006-0421-9
description: scientific article; zbMATH DE number 5172603