SCREEN CONFORMAL EINSTEIN LIGHTLIKE HYPERSURFACES OF A LORENTZIAN SPACE FORM

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

Einstein Lightlike Hypersurfaces of a Lorentz Space Form with a Semi-symmetric Non-metric Connection

We study Einstein lightlike hypersurfaces M of a Lorentzian space form M̃(c) admitting a semi-symmetric non-metric connection subject to the conditions; (1) M is screen conformal and (2) the structure vector field ζ of M̃ belongs to the screen distribution S(TM). The main result is a characterization theorem for such a lightlike hypersurface.

hypersurfaces with constant mean curvature in a lorentzian space form

Screen conformal half-lightlike submanifolds

We study some properties of a half-lightlike submanifoldM , of a semi-Riemannianmanifold, whose shape operator is conformal to the shape operator of its screen distribution. We show that any screen distribution S(TM) of M is integrable and the geometry of M has a close relation with the nondegenerate geometry of a leaf of S(TM). We prove some results on symmetric induced Ricci tensor and null s...

Hypersurfaces of a Sasakian space form with recurrent shape operator

Let $(M^{2n},g)$ be a real hypersurface with recurrent shapeoperator and tangent to the structure vector field $xi$ of the Sasakian space form$widetilde{M}(c)$. We show that if the shape operator $A$ of $M$ isrecurrent then it is parallel. Moreover, we show that $M$is locally a product of two constant $phi-$sectional curvaturespaces.