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Concircular vector fields on semi-Riemannian spaces

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Abstract

In this paper, we construct an analogue of concircular fields for semi-Riemannian spaces (i.e., for manifolds with degenerate metrics). We find a tensor criterion of spaces admitting the maximal number of concircular fields or having no such fields. We detect a gap in the distribution of dimensions of the space of concircular fields, which, in contrast to the corresponding gap in the case of pseudo-Riemannian manifolds, is lesser by 1. We also study some special types of concircular fields having no analogues for pseudo-Riemannian manifolds. The canonical form of the metric for some classes of semi-Riemannian spaces admitting concircular fields is obtained.

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Authors and Affiliations

  1. Finance Academy under the Government of the Russian Federation, Russia

    I. G. Shandra

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  1. I. G. Shandra
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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 31, Geometry, 2005.

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Shandra, I.G. Concircular vector fields on semi-Riemannian spaces. J Math Sci 142, 2419–2435 (2007). https://doi.org/10.1007/s10958-007-0184-4

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  • DOI: https://doi.org/10.1007/s10958-007-0184-4

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