Compact surfaces of constant Gaussian curvature in Randers manifolds

Randers Manifolds of Positive Constant Curvature

We prove that any simply connected and complete Riemannian manifold, on which a Randers metric of positive constant flag curvature exists, must be diffeomorphic to an odd-dimensional sphere, provided a certain 1-form vanishes on it. 1. Introduction. The geometry of Finsler manifolds of constant flag curvature is one of the fundamental subjects in Finsler geometry. Akbar-Zadeh [1] proved that, u...

Compact Constant Mean Curvature Surfaces with Low Genus

We describe numerical experiments that suggest the existence of compact constant mean curvature surfaces. Our surfaces come in three dihedrally symmetric families with the genus ranging from 3 to 5, 7 to 10, and 3 to 9, respectively; there are further surfaces with the symmetry of the Platonic polyhedra and genera 6, 12, and 30. We use the algorithm of Oberknapp and the second author that defin...

Surfaces of Constant Mean Curvature

On cohomogeneity one nonsimply connected 7-manifolds of constant positive curvature

In this paper, we give a classification of non simply connected seven dimensional Reimannian manifolds of constant positive curvature which admit irreducible cohomogeneity-one actions. We characterize the acting groups and describe the orbits. The first and second homo-topy groups of the orbits have been presented as well.

Constant k-curvature hypersurfaces in Riemannian manifolds

In [8], Rugang Ye proved the existence of a family of constant mean curvature hypersurfaces in an m+ 1-dimensional Riemannian manifold (M, g), which concentrate at a point p0 (which is required to be a nondegenerate critical point of the scalar curvature), moreover he proved that this family constitute a foliation of a neighborhood of p0. In this paper we extend this result to the other curvatu...