On the classification of the almost contact metric manifolds

Valentin A. Alexiev; Georgi T. Ganchev

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arXiv · 1110.4297

On the classification of the almost contact metric manifolds

Valentin A. Alexiev·Georgi T. Ganchev

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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, $α$-Sasakian, $α$-Kenmotsu, etc. manifolds fit nicely to these considerations. On the other hand, many new interesting classes of almost contact metric manifolds arise.

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Valentin A. Alexiev, Georgi T. Ganchev. 2011-10-19. On the classification of the almost contact metric manifolds. https://arxiv.org/abs/1110.4297

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