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Differential geometry on almost tangent manifolds

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Summary

We start from a tensor field Q of type (1, 1) defined in a2n-dimensional manifold M which satisfies Q2=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.

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Additional information

To ProfessorBeniamino Segre on his seventieth birthday

Entrata in Redazione il 7 giugno 1973.

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Yano, K., Davies, E.T. Differential geometry on almost tangent manifolds. Annali di Matematica 103, 131 (1975) doi:10.1007/BF02414150

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Keywords

  • Differential Geometry
  • Quaternion Structure
  • Tensor Field
  • Tangent Structure
  • Tangent Manifold