Geodesic
On Almost Contingent Manifolds of Second Class with Applications in Relativity
Canadian mathematical bulletin, Tome 21 (1978) no. 3, pp. 289-295

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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. 
Duggal, K. L. On Almost Contingent Manifolds of Second Class with Applications in Relativity. Canadian mathematical bulletin, Tome 21 (1978) no. 3, pp. 289-295. doi: 10.4153/CMB-1978-051-4
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     title = {On {Almost} {Contingent} {Manifolds} of {Second} {Class} with {Applications} in {Relativity}},
     journal = {Canadian mathematical bulletin},
     pages = {289--295},
     year = {1978},
     volume = {21},
     number = {3},
     doi = {10.4153/CMB-1978-051-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1978-051-4/}
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