منابع مشابه
The Special Hypersurfaces of Minkowski Space
Let x : (M, F ) →֒ (V n+1, F ) be a simply connected hypersurface in a Minkowski space (V n+1, F ). In this paper, using the Gauss formula of Chern connection on Finsler submanifolds, we shall prove that if x(p) is normal to Tp(M)(∀p ∈ M), then M with the induced metric is isometric to the standard Euclidean sphere.
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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...
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متن کاملMinkowski Type Problems for Convex Hypersurfaces in Hyperbolic Space
We consider the problem F = f(ν) for strictly convex, closed hypersurfaces in H and solve it for curvature functions F the inverses of which are of class (K).
متن کاملUmbilical hypersurfaces of Minkowski spaces
In this paper, by the Gauss equation of the induced Chern connection for Finsler submanifolds, we prove that if M is an umbilical hypersurface of a Minkowski space (V , F ), then either M is a Riemannian space form or a locally Minkowski space. AMS subject classifications: 53C60, 53C40
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1982
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1982-0660598-4