\(g\)-natural contact metrics on unit tangent sphere bundles
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 \(T_1M\).
scientific article; zbMATH DE number 5172603