Symmetries of null Geometry in Indefinite Kenmotsu Manifolds
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Submission date: 07. Jul. 2011
published in: Mediterranean journal of mathematics, 10 (2013) 2, p. 1079-1099
DOI number (of the published article): 10.1007/s00009-012-0205-5
MSC-Numbers: 53C15, 53C25, 53C50
Keywords and phrases: Indefinite Kenmostu manifold, Null hypersurface, η- conformal connection
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Null hypersurfaces have metrics with vanishing determinants and this degeneracy of these metrics leads to several difficulties. In this paper, null hypersurfaces of indefinite Kenmotsu space forms, tangent to the structure vector field, are studied with specific attention to locally symmetric, semi-symmetric and Ricci semi-symmetric null hypersurfaces. We show that locally symmetric and semi-symmetric null hypersurfaces are totally geodesic and parallel. These also hold for Ricci semi-symmetric null hypersurfaces, under a certain condition. We prove that, in null Einstein hypersurfaces of an indefinite Kenmotsu space form, tangent to the structure vector field, the local symmetry, semi-symmetry and Ricci semi-symmetry notions are equivalent. For totally contact umbilical null hypersurfaces, we show that there are η-Weyl connections adapted to the induced structure on the null hypersurface.