International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 2, Pages 257-266
Pseudo-Reimannian manifolds endowed with an almost para -structure
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 be a pseudo-Riemannian manifold of signature . One defines on an almost cosymplectic para -structure and proves that a manifold endowed with such a structure is -Ricci flat and is foliated by minimal hypersurfaces normal to , which are of Otsuki's type. Further one considers on a -dimensional involutive distribution and a recurrent vector field . It is proved that the maximal integral manifold of has as the mean curvature vector (up to ). If the complimentary orthogonal distribution of is also involutive, then the whole manifold is foliate. Different other properties regarding the vector field are discussed.