ON THE CLASSIFICATION OF THE ALMOST CONTACT METRIC MANIFOLDS

By Valentin A. Alexiev, G. Ganchev. 2011

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The vector space of the tensors 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 F into orthogonal components which are invariant under the action of U(n) × 1 is given. Using this decomposition there are found 12 natural basic classes of almost contact metric manifolds. The classes of cosymplectic, �-Sasakian, �-Kenmotsu, etc. manifolds fit nicely to these considerations. On the other hand, many new interesting classes of almost contact metric manifolds arise. 1. Preliminaries

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

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In Applied Mathematics

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