On the classes of almost Hermitian structures on the tangent bundle of an almost contact metric manifold
Copyright policy )On the classes of almost Hermitian structures on the tangent bundle of an almost contact metric manifold
If M is an almost contact metric manifold then by using some standard construction its tangent space TM becomes an almost Hermitian manifold. A classification for almost Hermitian manifolds was obtained by \textit{A. Gray} and \textit{L. M. Hervella} [Ann. Mat. Pura Appl., IV. Ser. 123, 35-58 (1980; Zbl 0444.53022)]. Following this classification \textit{J. A. Oubiña} [Publ. Math. 32, 187-193 (1983; Zbl 0611.53032)] has given a classification of almost contact manifolds. The main aim of this paper is to study those types of almost contact metric structures on M which appear when one considers various almost Hermitian structures on TM. The opposite connection is also investigated. Other interesting results are concerned with curvature identities.
curvature identities, almost Hermitian manifold, General geometric structures on manifolds (almost complex, almost product structures, etc.), almost contact metric manifold
curvature identities, almost Hermitian manifold, General geometric structures on manifolds (almost complex, almost product structures, etc.), almost contact metric manifold
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