Fe b 20 09 Examples of H - hypersurfaces in H n × R and geometric applications
نویسنده
چکیده
In this paper we describe all rotation H-hypersurfaces in Hn×R and use them as barriers to prove existence and characterization of certain vertical H-graphs and to give symmetry and uniqueness results for compact H-hypersurfaces whose boundary is one or two parallel submanifolds in slices. We also describe examples of translation H-hypersurfaces in Hn × R. In particular, for H < n−1 n , we obtain a complete non-entire vertical graph taking infinite boundary value data. Mathematics Subject Classification (2000): 53C42, 53C21
منابع مشابه
EXAMPLES OF H - HYPERSURFACES IN H n × R AND GEOMETRIC APPLICATIONS
In this paper we describe all rotation H-hypersurfaces in Hn × R and use them as barriers to prove existence and characterization of certain vertical H-graphs and to give symmetry and uniqueness results for compact H-hypersurfaces whose boundary is one or two parallel submanifolds in slices. We also describe examples of translation H-hypersurfaces in Hn × R. For n > 2 we obtain a complete embed...
متن کاملOn new types of contraction mappings in bipolar metric spaces and applications
Our aim is to present some common fixed point theorems in bipolar metric spaces via certain contractive conditions. Some examples have been provided to illustrate the effectiveness of new results. At the end, we give two applications dealing with homotopy theory and integral equations.
متن کاملLinear Weingarten hypersurfaces in a unit sphere
In this paper, by modifying Cheng-Yau$'$s technique to complete hypersurfaces in $S^{n+1}(1)$, we prove a rigidity theorem under the hypothesis of the mean curvature and the normalized scalar curvature being linearly related which improve the result of [H. Li, Hypersurfaces with constant scalar curvature in space forms, {em Math. Ann.} {305} (1996), 665--672].
متن کاملSpacelike hypersurfaces with constant $S$ or $K$ in de Sitter space or anti-de Sitter space
Let $M^n$ be an $n(ngeq 3)$-dimensional complete connected and oriented spacelike hypersurface in a de Sitter space or an anti-de Sitter space, $S$ and $K$ be the squared norm of the second fundamental form and Gauss-Kronecker curvature of $M^n$. If $S$ or $K$ is constant, nonzero and $M^n$ has two distinct principal curvatures one of which is simple, we obtain some charact...
متن کاملar X iv : 0 90 2 . 17 29 v 1 [ m at h . N T ] 1 0 Fe b 20 09 ON THE DIMENSION OF AG TRACE CODES
We determine the dimension of certain q-ary algebraic-geometric codes, extending previous results of Van Der Vlugt for p-ary algebraic-geometric trace codes.
متن کامل