EuDML | Browse

In this paper we study the topological and metric rigidity of hypersurfaces in $ℍ^{n + 1}$ , the $(n + 1)$ -dimensional hyperbolic space of sectional curvature $- 1$ . We find conditions to ensure a complete connected oriented hypersurface in $ℍ^{n + 1}$ to be diffeomorphic to a Euclidean sphere. We also give sufficient conditions for a complete connected oriented closed hypersurface with constant norm of the second fundamental form to be totally umbilic.

Topology and geometry of complete submanifolds in euclidean spaces

Qing-Ming Cheng (2005)

Banach Center Publications

This paper is a survey of results on topological structures and curvature structures of complete submanifolds in a Euclidean space.

Currently displaying 501 – 520 of 554

Previous Page 26 Next

Displaying 501 – 520 of 554

The Structure of Minimizing Hypersurfaces Mod 4.

The structure of single-periodic minimal surfaces.

The Tightness of Extrinsic Symmetric Submanifolds.

The tightness of tubes.

The topology of large $H$ -surfaces bounded by a convex curve

The Torsion Form of Submanifolds in EN.

The Trapping Property of Totally Geodesic Hyperplanes in Hadamard Spaces.

The triply periodic minimal surfaces of Alan Schoen and their constant mean curvature companions.

The Unknottedness of Minimal Embeddings.

The Weierstrass representation for complete minimal real Kaehler submanifolds of codimension two.

Three-dimensional slant submanifolds of $K$ -contact manifolds.

Tight and 0-Tight Polyhedral Embeddings of Surfaces.

Tight embeddings of simply connected 4-manifolds.

Tight immersions of highly connected manifolds.

Topological and metric rigidity teorems for hypersurfaces in a hyperbolic space

Topology and geometry of complete submanifolds in euclidean spaces

Total curvature for knotted surfaces.

Total curvature of manifolds in self-immersed manifolds.

Totale Absolutkrümmung von Hyperflächen

Totally geodesic foliations.

Currently displaying 501 – 520 of 554