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On Almost Contingent Manifolds of Second Class with Applications in Relativity

Published online by Cambridge University Press:  20 November 2018

K. L. Duggal
K. L. Duggal*
Affiliation:
Department of Mathematics, University of Windsor, Windsor, Ontario N9B 3P4, Canada
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D. E. Blair [1] has introduced the notion of K-manifolds as an analogue of the even dimensional Kähler manifolds and of the odd dimensional quasi-Sasakian manifolds. These manifolds have been studied with respect to a positive definite metric. In this paper, we study a more general case of if-manifolds carrying an arbitrary non-degenerate metric, in particular, a metric of Lorentz signature. This theory is then applied within the frame-work of general relativity. Using the Ruse-Synge classification [8, 9] of non-null electromagnetic fields with source, we develop a geometric proof for the existence of either two space like or one space like and one time like Killing vector fields on the space-time manifold.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 21 , Issue 3 , 01 September 1978 , pp. 289 - 295
Copyright
Copyright © Canadian Mathematical Society 1978

References

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