$L_k$-BIHARMONIC HYPERSURFACES IN THE EUCLIDEAN SPACE
نویسندگان
چکیده
منابع مشابه
Lk-BIHARMONIC HYPERSURFACES IN THE EUCLIDEAN SPACE
Chen conjecture states that every Euclidean biharmonic submanifold is minimal. In this paper we consider the Chen conjecture for Lk-operators. The new conjecture (Lk-conjecture) is formulated as follows: If Lkx = 0 then Hk+1 = 0 where x : M → R is an isometric immersion of a Riemannian manifold M into the Euclidean space R, Hk+1 is the (k+1)-th mean curvature of M , and Lk is the linearized ope...
متن کامل$L_k$-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...
متن کاملTangent Bundle of the Hypersurfaces in a Euclidean Space
Let $M$ be an orientable hypersurface in the Euclidean space $R^{2n}$ with induced metric $g$ and $TM$ be its tangent bundle. It is known that the tangent bundle $TM$ has induced metric $overline{g}$ as submanifold of the Euclidean space $R^{4n}$ which is not a natural metric in the sense that the submersion $pi :(TM,overline{g})rightarrow (M,g)$ is not the Riemannian submersion. In this paper...
متن کامل$l_k$-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...
متن کاملBiharmonic Hypersurfaces in 4-dimensional Space Forms
We investigate proper biharmonic hypersurfaces with at most three distinct principal curvatures in space forms. We obtain the full classification of proper biharmonic hypersurfaces in 4-dimensional space forms.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Taiwanese Journal of Mathematics
سال: 2015
ISSN: 1027-5487
DOI: 10.11650/tjm.19.2015.4830