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- W2562557346 abstract "In (4), Y.-C Wong conjectured that the covariant derivative of the recurrence covector field of an anely connected recurrent space An with a torsion-free connection will be symmetric if and only if the Ricci tensor of An 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 Recurrent Riemannian manifolds and in (8), Singh and Khan studied the nature of the recurrence vectors appearing in the definition of the Gener- alized 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." @default.
- W2562557346 created "2017-01-06" @default.
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- W2562557346 date "2006-01-01" @default.
- W2562557346 modified "2023-09-24" @default.
- W2562557346 title "On generalized recurrent Weyl spaces and Wong's conjecture" @default.
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