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Totally geodesic foliations on semi-Riemannian manifolds. (English) Zbl 0910.53018

The author studies the case of orthogonal foliations \({\mathcal I}\) and \({\mathcal I}'\) over a complete semi-Riemannian manifold \((M,g)\) of dimension \((m+n)\). The foliation \({\mathcal I}\) is either spacelike or timelike, while the foliation \({\mathcal I}^\perp\) is totally geodesic. Under some additional conditions, the foliation \({\mathcal I}\) will also be totally geodesic.

MSC:

53C12 Foliations (differential geometric aspects)
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
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