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...

In this paper, we attain the problem of constructing hypersurfaces from a given geodesic curve in 4D Euclidean space E4. Using Serret–Frenet frame curve, express hypersurface as linear combination and analyze necessary sufficient conditions for that to be geodesic. We illustrate method by presenting some examples.

The existence of closed hypersurfaces of prescribed curvature in semi-riemannian manifolds is proved provided there are barriers.

A real n-dimensional homogeneous polynomial f (x) of degree m and a real constant c define an algebraic hypersurface S whose points satisfy f (x) = c. The polynomial f can be represented by Axm where A is a real mth order n-dimensional supersymmetric tensor. In this paper, we define rank, base index and eigenvalues for the polynomial f , the hypersurface S and the tensor A. The rank is a nonneg...

We obtain a characterization for a compact Hopf hypersurface in the nearly Kaehler sphere S using a pinching on the scalar curvature of the hypersurface. It has been also observed that the totally geodesic sphere S in S has induced Sasakian structure as a hypersurface of the nearly Kaehler sphere S. M.S.C. 2000: 53C20, 53C45.