International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 2, Pages 257-266

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

Vladislav V. Goldberg and Radu Rosca

Department of Mathematics, New Jersey Institute of Technology, 323 Dr. Martin Luther King Jr. Boulevard, Newark 07102, N.J., USA

Received 27 December 1983

Copyright © 1985 Vladislav V. Goldberg and Radu Rosca. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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(n1)-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(n1)). 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.