Comparison of metrics on three-dimensional Lie groups
We study local equivalence of left-invariant metrics with the same curvature on Lie groups and of dimension three, when is unimodular and is non-unimodular.
Comparison principles and Liouville theorems for prescribed mean curvature equations in unbounded domains
Comparison principles for hypersurfaces of prescribed mean curvature.
Comparison theorems and hypersurfaces.
Comparison theorems for compact symmetric spaces
Comparison Theory for Riccati equations.
Compatible complex structures on twistor space
Let be a Riemannian 4-manifold. The associated twistor space is a bundle whose total space admits a natural metric. The aim of this article is to study properties of complex structures on which are compatible with the fibration and the metric. The results obtained enable us to translate some metric properties on (scalar flat, scalar-flat Kähler...) in terms of complex properties of its twistor space .
Compatible flat metrics.
Complément à la théorie d'Arnold de l'indice de Maslov
Complément à la théorie d'Arnold de l'indice de Maslov
Complete classification of parallel Lorentz surfaces in neutral pseudo hyperbolic 4-space
A Lorentz surface of an indefinite space form is called a parallel surface if its second fundamental form is parallel with respect to the Van der Waerden-Bortolotti connection. Such surfaces are locally invariant under the reflection with respect to the normal space at each point. Parallel surfaces are important in geometry as well as in general relativity since extrinsic invariants of such surfaces do not change from point to point. Recently, parallel Lorentz surfaces in 4D neutral pseudo Euclidean...
Complete classification of spatial surfaces with parallel mean curvature vector in arbitrary non-flat pseudo-Riemannian space forms
Submanifolds with parallel mean curvature vector play important roles in differential geometry, theory of harmonic maps as well as in physics. Spatial surfaces in 4D Lorentzian space forms with parallel mean curvature vector were classified by B. Y. Chen and J. Van der Veken in [9]. Recently, spatial surfaces with parallel mean curvature vector in arbitrary pseudo-Euclidean spaces are also classified in [7]. In this article, we classify spatial surfaces with parallel mean curvature vector in pseudo-Riemannian...
Complete classification of surfaces with a canonical principal direction in the Euclidean space 3
In the present paper we classify all surfaces in 3 with a canonical principal direction. Examples of this type of surfaces are constructed. We prove that the only minimal surface with a canonical principal direction in the Euclidean space 3 is the catenoid.
Complete Finsler manifolds and adapted coordinates.
Complete gradient Ricci solitons
For complete gradient Ricci solitons we state necessary conditions for a non-trivial soliton structure in terms of intrinsic curvature invariants.
Complete Homogeneous Riemannian Manifolds of Negative Sectional Curvature.
Complete Hypersurfaces in the Space Form with Three Principal Curvatures.
Complete Hypersurfaces of R4 with Constant Mean Curvature.
Complete hypersurfaces with constant scalar curvature in a hyperbolic space.
Complete hypersurfaces with constant scalar curvature in a sphere
In this paper, by using Cheng-Yau’s self-adjoint operator , we study the complete hypersurfaces in a sphere with constant scalar curvature.