WEAKLY COMPLETE WAVE FRONTS WITH ONE PRINCIPAL CURVATURE CONSTANT

Principal Lines on Surfaces Immersed with Constant Mean Curvature

Configurations of lines of principal curvature on constant mean curvature immersed surfaces are studied. Analytical models for these configurations near general isolated umbilical points and particular types of ends are found. From the existence of transversal invariant measures for the foliations by principal lines, established here, follows that the union of recurrent lines of principal curva...

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

Isoperimetric Inequalities for Wave Fronts and a Generalization of Menzin’s Conjecture for Bicycle Monodromy on Surfaces of Constant Curvature

The classical isoperimetric inequality relates the lengths of curves to the areas that they bound. More specifically, we have that for a smooth, simple closed curve of length L bounding area A on a surface of constant curvature c, L2 ≥ 4πA− cA2 with equality holding only if the curve is a geodesic circle. We prove generalizations of the isoperimetric inequality for both spherical and hyperbolic...

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.

The Moduli Space of Complete Embedded Constant Mean Curvature Surfaces

We examine the space of surfaces in R which are complete, properly embedded and have nonzero constant mean curvature. These surfaces are noncompact provided we exclude the case of the round sphere. We prove that the space Mk of all such surfaces with k ends (where surfaces are identified if they differ by an isometry of R) is locally a real analytic variety. When the linearization of the quasil...