Hypersurfaces with parallel Laguerre form in R

Hoph Hypersurfaces of Sasakian Space Form with Parallel Ricci Operator Esmaiel Abedi, Mohammad Ilmakchi Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran

Let M^2n be a hoph hypersurfaces with parallel ricci operator and tangent to structure vector field in Sasakian space form. First, we show that structures and properties of hypersurfaces and hoph hypersurfaces in Sasakian space form. Then we study the structure of hypersurfaces and hoph hypersurfaces with a parallel ricci tensor structure and show that there are two cases. In the first case, th...

Laguerre Geometry of Hypersurfaces in Rn

Laguerre geometry of surfaces in R is given in the book of Blaschke [1], and have been studied by E.Musso and L.Nicolodi [5], [6], [7], B. Palmer [8] and other authors. In this paper we study Laguerre differential geometry of hypersurfaces in Rn. For any umbilical free hypersurface x : M → Rn with non-zero principal curvatures we define a Laguerre invariant metric g on M and a Laguerre invarian...

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.

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

Pseudo-Parallel submanifolds

Pseudo-parallel (shortly PP) submanifolds are defined as a generalization of semi-parallel (shortly SP ) submanifolds and as extrinsic analogue of pseudo-symmetric (shortly PS) manifolds (in the sense of R. Deszcz) [1], [26]. Asperti et al [1] obtained a description of PP hypersurfaces in space form as quasiumbilic hypersurfaces or cyclids of Dupin and studied PP surfaces with maximal first nor...