On the classification of the almost contact metric manifolds

Abstract

The vector space of the tensors $\mathcal{F}$ of type (0,3) having the same symmetries as the covariant derivative of the fundamental form of an almost contact metric manifold is considered. A scheme of decomposition of $\mathcal{F}$ into orthogonal components which are invariant under the action of $U(n)\times 1$ is given. Using this decomposition there are found 12 natural basic classes of almost contact metric manifolds. The classes of cosymplectic, $\alpha$-Sasakian, $\alpha$-Kenmotsu, etc. manifolds fit nicely to these considerations. On the other hand, many new interesting classes of almost contact metric manifolds arise.

7 pages; Mathematics and Education in Mathematics, 1986

Cited by in corpus (5)

• Killing-Yano tensors and some applications
• A classification of the torsion tensors on almost contact manifolds with B-metric
• Pure spinors, intrinsic torsion and curvature in odd dimensions
• Natural Connections with Totally Skew-Symmetric Torsion on Manifolds with Almost Contact 3-Structure and Metrics of Hermitian-Norden Type
• Subclasses of the Conformal Almost Contact Metric Manifolds