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- Title
RIGGED NULL HYPERSURFACES IN ALMOST PARACONTACT METRIC MANIFOLDS.
- Authors
NGAKEU, F.; DJOMAKO, A. C.; NDOMBOL, BITJONG
- Abstract
Given an almost paracontact metric manifold (M;&#966, &#951, &#950, g), we study lightlike hypersurfacesM of the semi-Riemannian manifold (M; g) transversal to the structure vector field ζ. The latter is then a rigging for M and defines a null section E of the radical distribution of M and a screen distribution which turns out to be always semi-invariant. We show that leaves of an integrable screen distribution in such hypersurfaces M are almost paracontact metric manifolds too. When the ambient space (M;&#966, &#951, &#950, g) is para-Sasakian, we show that the screen distribution cannot be conformal and that E is a geodesic vector field in (M;r); where r is the connection induced on M by Levi-Civita connection of g and the local null rigging N = ζ - 1/2 2E. We also find necessary and sufficient conditions for the leaves of the screen distribution to be para-Sasakian too and finally we investigate integrability conditions for some additional distributions induced on M by the structure (M;&#966, &#951, &#950, g).
- Subjects
MANIFOLDS (Mathematics); HYPERSURFACES; VECTOR fields; RIEMANNIAN manifolds; GEOMETRIC connections
- Publication
Gulf Journal of Mathematics, 2019, Vol 7, Issue 2, p37
- ISSN
2309-4966
- Publication type
Article
- DOI
10.56947/gjom.v7i2.190