Lorentzian a-sasakian manifolds

In this thesis, Sasakian manifolds and Lorentzian α − Sasakian manifolds are examined.Thesis falls into 3 sections. In te first section includes somefundamental concepts and resultswhich will be used in other sections. In the second section, we study some fundamentaldescribtions, thearies and results about the Sasakian manifolds. In the last section, Lorentzianα − Sasakian manifolds are studied, and some of the conditions of curvation are examined, andsome of the reasanable results related to it are attained.In the first section, some of the fundamental concepts such as afin convection, Riemanncurvaton tensor, Eistein manifold, Weyl-conformal tensor, conormal flat maniold, Riccicurvation tensor are introduced.In the second section, Sasakian manifolds are introduced by giving some of thefundamental concept such as nearly contact manifold, riemann metric, Lie involution, Killingvector area, K-contact manifold, and inthe last section Lorentzian α − Sasakian.In the last section, basic theories and definitions about Lorentzian α − Sasakianmanifolds and aguivalences used to obtain conditions of curvation are given. Remarkable resultsare attained by proving these theories by mentioning about all these information.Key Words : Conctact metric manifold, Curvation tensor, Einstein manifold, K-conctactmanifold, Lorentzian α − Sasakian manifold, Ricci curvation tensor, Sasakian manifold,