On generalized recurrent Weyl spaces and Wong's conjecture

Elif¨ozkara Elif¨, Elif¨ozkara Canfes
unpublished
In [4], Y.-C Wong conjectured that the covariant derivative of the recurrence covector field of an affinely connected recurrent space A n with a torsion-free connection will be symmetric if and only if the Ricci tensor of A n is symmetric. In [6], it is proved that for a Recurrent Weyl space with a non-vanishing scalar curvature the covariant derivative of the recurrence vector field is symmetric if and only if the Weyl mani-fold is locally Riemannian. In [7], De and Guha introduced Generalized
more » ... Recurrent Riemannian manifolds and in [8], Singh and Khan studied the nature of the recurrence vectors appearing in the definition of the Generalized recurrent Riemannian manifold. In the present work, Generalized Recurrent Weyl manifolds are defined and proved that for a Generalized Recurrent Weyl manifold with a non-vanishing constant scalar curvature the covariant derivatives of the recurrence vector fields are both symmetric if and only if the Weyl manifold is locally Riemannian. Moreover, some results about hypersurfaces of Generalized Recurrent Weyl manifolds are obtained. M.S.C. 2000: 53B15, 53B25.
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