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Second order parallel tensor in real and complex space forms

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  • Ramesh Sharma

Abstract

Levy's theorem ‘A second order parallel symmetric non-singular tensor in a real space form is proportional to the metric tensor’ has been generalized by showing that it holds even if one assumes the second order tensor to be parallel (not necessarily symmetric and non-singular) in a real space form of dimension greater than two. Analogous result has been established for a complex space form. It has been shown that an affine Killing vector field in a non-flat complex space form is Killing and analytic.

Suggested Citation

  • Ramesh Sharma, 1989. "Second order parallel tensor in real and complex space forms," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 12, pages 1-4, January.
    • Handle: RePEc:hin:jijmms:209894
    DOI: 10.1155/S0161171289000967
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    Cited by:

    1. Mircea Crasmareanu, 2012. "Parallel tensors and Ricci solitons in N (k)-quasi Einstein manifolds," Indian Journal of Pure and Applied Mathematics, Springer, vol. 43(4), pages 359-369, August.
    2. Mukut Mani Tripathi & Punam Gupta & Jeong-Sik Kim, 2012. "Index of Quasiconformally Symmetric Semi-Riemannian Manifolds," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-14, July.

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