Generalized condensers and conformal properties of riemannian manifolds with at least two ends
Generalized symmetric spaces and minimal models
We prove that any compact simply connected manifold carrying a structure of Riemannian 3- or 4-symmetric space is formal in the sense of Sullivan. This result generalizes Sullivan's classical theorem on the formality of symmetric spaces, but the proof is of a different nature, since for generalized symmetric spaces techniques based on the Hodge theory do not work. We use the Thomas theory of minimal models of fibrations and the classification of 3- and 4-symmetric spaces.
Generalized symmetric spaces (Preliminary communication)
Geodesic Mappings on Compact Riemannian Manifolds with Conditions on Sectional Curvature
Geodesic monotone vector fields.
Geodesics on a central symmetric warped product manifold.
Geodesics on the tangent sphere bundles over space forms.
Geodesics Satisfying General Boundary Conditions
Géodésiques pour des métriques riemanniennes semi-continues inférieurement
Geometric finiteness theorem via controlled topology (Erratum).
Geometric finiteness theorems via controlled topology.
Geometric P.D.E.'s with isolated singularities.
Geometric superrigidity.
Géométrie conforme en dimension : ce que l’analyse nous apprend
Cet article présente les idées, les outils et les résultats qui ont permis à Chang S.-Y. A., M. Gursky et Yang P. de donner une caractérisation intégrale conforme de la sphère standard en dimension 4. Nous démarrons avec une généralisation à cette dimension de la formule de Polyakov pour les déterminants régularisés, que nous utilisons ensuite pour résoudre des problèmes du type “Yamabe” pour des polynômes quadratiques en la courbure de Ricci. Nous introduisons au passage le concept de paire conforme,...
Géométrie systolique et métriques polyèdrales sur les 3-variétés de Bieberbach
La systole d’une variété riemannienne compacte non simplement connexe est la plus petite longueur d’une courbe fermée non contractile ; le rapport systolique est le quotient . Sa borne supérieure, sur l’ensemble des métriques riemanniennes, est fini pour une large classe de variétés, dont les .On étudie le rapport systolique optimal des variétés de Bieberbach compactes, orientables de dimension qui ne sont pas des tores, et on démontre en utilisant des constructions de métriques polyèdrales...
Geometrische Methoden zur Gewinnung von A-Priori-Schranken für harmonische Abbildungen.
Geometrodynamics of some non-relativistic incompressible fluids.
In some previous papers [1, 2] we proposed a geometric formulation of continuum mechanics, where a continuous body is seen as a suitable differentiable fiber bundle C on the Galilean space-time M, beside a differential equation of order k, Ek(C), on C and the assignement of a frame Psi on M. This approach allowed us to treat continuum mechanics as a unitary field theory and to consider constitutive and dynamical properties in a more natural way. Further, the particular intrinsic geometrical framework...
Geometry of Mus-Sasaki metric
In this paper, we introduce the Mus-Sasaki metric on the tangent bundle as a new natural metric non-rigid on . First we investigate the geometry of the Mus-Sasakian metrics and we characterize the sectional curvature and the scalar curvature.
Global models of Riemannian metrics.
In this paper we give certain Riemannian metrics on the manifolds Sn-1 x S1 and Sn (n ≥ 2), which have the property to determine these manifolds, up to diffeomorphisms.The global expressions used for Riemannian metrics are based on the global expression for exterior forms studied in [4]. In [3] one finds certain metrics using global expressions that differ from the type we propose.To some extent, Theorem 3 is a generalization for metrics in an arbitrary dimension, of a theorem proved in [2] for...
Global pinching theorems for minimal submanifolds in spheres
Let M be a compact submanifold with parallel mean curvature vector embedded in the unit sphere . By using the Sobolev inequalities of P. Li to get estimates for the norms of certain tensors related to the second fundamental form of M, we prove some rigidity theorems. Denote by H and the mean curvature and the norm of the square length of the second fundamental form of M. We show that there is a constant C such that if , then M is a minimal submanifold in the sphere with sectional curvature...