Singularity analysis of pseudo null hypersurfaces and pseudo hyperbolic hypersurfaces

Pseudo Ricci symmetric real hypersurfaces of a complex projective space

Pseudo Ricci symmetric real hypersurfaces of a complex projective space are classified and it is proved that there are no pseudo Ricci symmetric real hypersurfaces of the complex projective space CPn for which the vector field ξ from the almost contact metric structure (φ, ξ, η, g) is a principal curvature vector field.

Hopf Hypersurfaces of Small Hopf Principal Curvature in Ch

Using the methods of moving frames and exterior differential systems, we show that there exist Hopf hypersurfaces in complex hyperbolic space CH with any specified value of the Hopf principal curvature α less than or equal to the corresponding value for the horosphere. We give a construction for all such hypersurfaces in terms of Weierstrass-type data, and also obtain a classification of pseudo...

$L_k$-biharmonic spacelike hypersurfaces in Minkowski $4$-space $mathbb{E}_1^4$

Biharmonic surfaces in Euclidean space $mathbb{E}^3$ are firstly studied from a differential geometric point of view by Bang-Yen Chen, who showed that the only biharmonic surfaces are minimal ones. A surface $x : M^2rightarrowmathbb{E}^{3}$ is called biharmonic if $Delta^2x=0$, where $Delta$ is the Laplace operator of $M^2$. We study the $L_k$-biharmonic spacelike hypersurfaces in the $4$-dimen...

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

Biharmonic Space-like Hypersurfaces in Pseudo-riemannian Space

We classify the space-like biharmonic surfaces in 3dimension pseudo-Riemannian space form, and construct explicit examples of proper biharmonic hypersurfaces in general ADS space.