Second order parallel tensor in real and complex space forms

Ramesh Sharma

International Journal of Mathematics and Mathematical Sciences, 1989, vol. 12, 1-4

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.

Date: 1989
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:209894

DOI: 10.1155/S0161171289000967

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