The Scalar Curvature of Minimal Hypersurfaces in Spheres.
Si determina lo spettro di un operatore di Laplace di una «spherical space form» e si studia l’influenza di tale spettro su .
We prove that if the sectional curvature, , of a compact 6-manifold without boundary satisfies then its third (real) Betti number is zero.
An explicit classification of the spaces in the title is given. The resulting spaces are locally products or locally warped products of the real line and two-dimensional spaces of constant curvature.
This paper is motivated by the open problem whether a three-dimensional curvature homogeneous hypersurface of a real space form is locally homogeneous or not. We give some partial positive answers.
In this paper we study the topological and metric rigidity of hypersurfaces in , the -dimensional hyperbolic space of sectional curvature . We find conditions to ensure a complete connected oriented hypersurface in 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.
In this paper, we consider the problem of the existence of conformal metrics with prescribed scalar curvature on the standard sphere S n, n ≥ 3. We give new existence and multiplicity results based on a new Euler-Hopf formula type. Our argument also has the advantage of extending well known results due to Y. Li [16].