On conformally Recurrent Kahlerian-Weyl Spaces
by
Fatma Ozdemir
Istanbul Technical University
Coauthors: Gulcin Civi Yildirim (Istanbul Technical University)

Abstract

An m-dimensional manifold W_m(g_ij, T_k)  with a conformal metric tensor g_ij and a symmetric connection Ñ_k is called a Weyl space if the compatibility condition Ñ_k g_ij-2 T_k g_ij=0  is satisfied, where T_k is a covariant vector field.

If the Weyl space W_m admits an almost Hermitian structure F^j_i that satisfies [(Ñ)\dot]_k F^j_i=0   (for all i, j, k)  then W_m is called a Kahlerian space.

We consider   an m-dimensional Weyl space W_m  (m=2n) with Kahlerian structure. Let R_ijkl and F^ij=g^ih F^j_h be the covariant curvature tensor of weight {2} and skew-symmetric tensor of type (2, 0) of weight {-2} of W_m, respectively. Define the tensor G_ij of weight {0} by G_ij=H_ij-H_ji, where H_ij=¹/₂ R_ijklF^kl.

In this work, the properties related with the tensors H_ij and G_ij are given and it is proved that G_ij is proportional to F_ij if and only if the space W_m is an Einstein-Weyl space. Furthermore, for conformally recurrent Kahlerian-Weyl space we obtained that Kahlerian Weyl space will be a conformally recurrent if and only if it is a recurrent Weyl space.

Date received: July 17, 2002