Geodesic
Degenerate Riemannian metrics
Matematičeskie zametki, Tome 18 (1975) no. 5, pp. 767-774 Cet article a éte moissonné depuis la source Math-Net.Ru

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We give a criterion for the existence of a degenerate Riemannian metric on a paracompact $C^\infty$ manifold. We give a criterion for the existence of a corresponding connection without torsion on manifolds with degenerate Riemannian metrics. 
@article{MZM_1975_18_5_a12,
     author = {I. V. Bel'ko},
     title = {Degenerate {Riemannian} metrics},
     journal = {Matemati\v{c}eskie zametki},
     pages = {767--774},
     year = {1975},
     volume = {18},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1975_18_5_a12/}
}
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I. V. Bel'ko. Degenerate Riemannian metrics. Matematičeskie zametki, Tome 18 (1975) no. 5, pp. 767-774. http://geodesic.mathdoc.fr/item/MZM_1975_18_5_a12/