A criterion for foliations with transverse linear connection to be pseudo-Riemannian
N. I. Zhukova1, K. I. Sheina2
| Annotation | We obtain necessary and sufficient conditions for a foliation of codimension $q$ on $n$-dimensional manifold with transverse linear connection to admit a transverse invariant pseudo-Riemannian metric of a given signature which is parallel with the respect to the indicated connection. In particular we obtain a criterion for a foliation with transverse linear connection to be Riemannian foliation. |
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| Keywords | foliation, linear connection, holonomy group of a connection, the germ holonomy group of a leaf |
1N
2Professor of сhair of fundamental mathematics, National Research University Higher School of Economics, Nizhny Novgorod; nzhukova@hse.ru
3Research assistant of сhair of fundamental mathematics, National Research University Higher School of Economics, Nizhny Novgorod; ksheina@hse.ru
Citation: N. I. Zhukova, K. I. Sheina, "[A criterion for foliations with transverse linear connection to be pseudo-Riemannian]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,18:2 (2016) 30–40 (In Russian)
