The classification of 3-dimensional Lorentzian affine hypersurfaces with parallel cubic form

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

hypersurfaces with constant mean curvature in a lorentzian space form

Hypersurfaces with parallel Laguerre form in R

For a given (n − 1)-dimensional hypersurface x : M → R, consider the Laguerre form Φ, the Laguerre tensor L and the Laguerre second fundamental form B of the immersion x. In this article, we address the case when the Laguerre form of x is parallel, i.e., ∇Φ ≡ 0. We prove that ∇Φ ≡ 0 is equivalent to Φ ≡ 0, provided that either L+λB+μg = 0 for some smooth function λ and μ, or x has constant Lagu...

Centroaffine Surfaces with parallel traceless Cubic Form

In this paper, we classify the centroaffine surfaces with parallel cubic Simon form and the centroaffine minimal surfaces with complete positive definite flat metric.

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.