PROJECTIVE-RECURRENT VIASMAN-GRAY MANIFOLD
HABEEB M. ABOOD *
Department of Mathematic, College of Education for Pure Sciences, Basra University, Basra, Iraq
HADEEL G. ABD ALI
Department of Mathematic, College of Education for Pure Sciences, Basra University, Basra, Iraq
*Author to whom correspondence should be addressed.
Abstract
The purpose of this work is to study the geometric properties of projective tensor of Viasman-Gray manifold. The necessary condition that the Viasman-Gray manifold is projective para-kahler manifold has been found. The projective-recurrent Viasman-Gray manifold has been studied, in particular, it has been proved the projective-recurrent Viasman-Gray manifold is either projective symmetrical manifold or it is a locally conformal Kähler manifold. Finally, an application about the projective-recurrent of Viasman-Gray manifold has been given.
Keywords: Almost Hermitian manifold, Viasman-Gray manifold, projective-recurrent tensor