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On lightlike geometry in indefinite Kenmotsu manifolds
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Abstract
We investigate some geometric aspects of lightlike hypersurfaces of indefinite Kenmotsu manifolds, tangent to the structure vector field, by paying attention to the geometry of leaves of integrable distributions. Theorems on parallel vector fields, Killing distribution, geodesibility of their leaves are obtained. The geometric configuration of such lightlike hypersurfaces and leaves of its screen integrable distributions are established. We show that no totally contact umbilical leaf of a screen integrable distribution of a lightlike hypersurface can be an extrinsic sphere. We also prove that the geometry of any leaf of an integrable distribution is closely related to the geometry of a normal bundle.
Title: On lightlike geometry in indefinite Kenmotsu manifolds
Description:
Abstract
We investigate some geometric aspects of lightlike hypersurfaces of indefinite Kenmotsu manifolds, tangent to the structure vector field, by paying attention to the geometry of leaves of integrable distributions.
Theorems on parallel vector fields, Killing distribution, geodesibility of their leaves are obtained.
The geometric configuration of such lightlike hypersurfaces and leaves of its screen integrable distributions are established.
We show that no totally contact umbilical leaf of a screen integrable distribution of a lightlike hypersurface can be an extrinsic sphere.
We also prove that the geometry of any leaf of an integrable distribution is closely related to the geometry of a normal bundle.
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