On the Geometry of Complex-Contact Riemannian Submersion
S. Longwap *
Department of Mathematics, Faculty of Natural Sciences, University of Jos, P.M.B. 2084, Plateau State, Nigeria.
P. T. Ajai
Department of Mathematics, Faculty of Natural Sciences, Plateau State University, Bokkos, Plateau State, Nigeria.
N. Homti
Department of Mathematics, Faculty of Natural Sciences, University of Jos, P.M.B. 2084, Plateau State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
This paper gives the structure equations of a complex-contact Riemannian submersion and establish that the fiber of this submersion is a contact metric submanifold of the total space. We investigate the vertical and horizontal distributions and obtain necessary and sufficient conditions for the distributions to be totally geodesic foliations. We also obtain some necessary and sufficient conditions of the submersion to be a totally geodesic map.
Keywords: Riemannian submersion, almost Hermitian manifold, contact metric manifold.