International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 2, Pages 339-350
doi:10.1155/S0161171284000363
Contact co-isotropic CR submanifolds of a pseudo-Sasakian manifold
Vladislav V. Goldberg
and Radu Rosca
Department of Mathematics, N.J. Institute of Technology, 323 M.L. King Jr. Boulevard Newark, 07102, N.J., USA
Abstract
It is proved that any co-isotropic submanifold M of a pseudo-Sasakian manifold M˜(U,ξ,η˜,g˜) is a CR submanifold (such submanfolds are called CICR submanifolds) with involutive vertical distribution ν1. The leaves M1 of D1 are isotropic and M is ν1-totally geodesic. If M is foliate, then M is almost minimal. If M is Ricci D1-exterior recurrent, then M receives two contact Lagrangian foliations. The necessary and sufficient conditions for M to be totally minimal is that M be contact D1-exterior recurrent.