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Differential geometry on almost tangent manifolds

1975; Springer Science+Business Media; Volume: 103; Issue: 1 Linguagem: Inglês

10.1007/bf02414150

1618-1891

Kentaro Yano, E. T. Davies,

Tensor decomposition and applications

We start from a tensor field Q of type (1, 1) defined in a2n-dimensional manifold M which satisfies Q 2=0 and has rank n. The tensor field Q defines an almost tangent structure in M. We then introduce another tensor field P of the same type and having properties similar to those of Q. We then define and study the tensors H=PQ, V=QP, J=P−Q, K=P+Q, L=PQ−QP, (J, K, L) defining an almost quaternion structure of the second kind on M. We study the differential geometry on almost tangent manifolds in terms of these tensors.