delN-EINSTEIN ALMOST CONTACT METRIC MANIFOLDS

On an almost contact metric manifold M, an N-connection del(N) defined by the pair (del, N), where del is the interior metric connection and N: TM -> TM is an endomorphism of the tangent bundle of the manifold M such that N(xi)over-right-arrow = (0)over-right-arrow, N (D) subset of D , is considered. Special attention is paid to the case of a skew-symmetric N-connection del(N), which means that the torsion of an N-connection considered as a trivalent covariant tensor is skew-symmetric. Such a connection is uniquely defined and corresponds to the endomorphism N = 2 psi, where the endomorphism psi is defined by the equality omega(X,Y) = g(psi X ,Y) and is called in this work the second structure endomorphism of an almost contact metric manifold. The notion of a del(N)-Einstein almost contact metric manifold is introduced. For the case N = 2 psi, conditions under which almost contact manifolds are del(N)-Einstein manifolds are found.