Pseudo-Reimannian manifolds endowed with an almost para f -structure

Vladislav V. Goldberg and Radu Rosca

International Journal of Mathematics and Mathematical Sciences, 1985, vol. 8, 1-10

Abstract:

Let M ˜ ( U , Ω ˜ , η ˜ , ξ , g ˜ ) be a pseudo-Riemannian manifold of signature ( n + 1 , n ) . One defines on M ˜ an almost cosymplectic para f -structure and proves that a manifold M ˜ endowed with such a structure is ξ -Ricci flat and is foliated by minimal hypersurfaces normal to ξ , which are of Otsuki's type. Further one considers on M ˜ a 2 ( n − 1 ) -dimensional involutive distribution P ⊥ and a recurrent vector field V ˜ . It is proved that the maximal integral manifold M ⊥ of P ⊥ has V as the mean curvature vector (up to 1 / 2 ( n − 1 ) ). If the complimentary orthogonal distribution P of P ⊥ is also involutive, then the whole manifold M ˜ is foliate. Different other properties regarding the vector field V ˜ are discussed.

Date: 1985
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:292031

DOI: 10.1155/S016117128500028X

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