On the classification of the almost contact metric manifolds

Details On the classification of the almost contact metric manifolds On the classification of the almost contact metric manifolds

2011-10-19

arxiv.org/abs/1110.4297v1

Proc. Fifteenth Conf. Union of the Bulgarian Mathematicians, Sunny Beach, April 2-6,1986,155-161

Mathematics

Differential Geometry

7 pages; Mathematics and Education in Mathematics, 1986

Scientific paper

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.

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