Rigidity theorems for surfaces in euclidean space

Characterizations of Slant Ruled Surfaces in the Euclidean 3-space

In this study, we give the relationships between the conical curvatures of ruled surfaces generated by the unit vectors of the ruling, central normal and central tangent of a ruled surface in the Euclidean 3-space E^3. We obtain differential equations characterizing slant ruled surfaces and if the reference ruled surface is a slant ruled surface, we give the conditions for the surfaces generate...

Sphere Rigidity in the Euclidean Space Julien

In this article, we prove new stability results for almost-Einstein hypersurfaces of the Euclidean space, based on previous eigenvalue pinching results. Then, we deduce some comparable results for almostumbilic hypersurfaces and new characterizations of geodesic spheres.

Minimal Surfaces in Euclidean Space

Local Rigidity of Surfaces in Space Forms

We prove that isometric embeddings of closed, embedded surfaces in R are locally rigid, i.e. they admit no non-trivial local isometric deformations, answering a question in classical differential geometry. The same result holds for abstract surfaces embedded in constant curvature 3-manifolds, provided a mild condition on the fundamental group holds.

Embeddings of Surfaces in Euclidean Three-space