Differential geometric structures of stable state feedback systems with dual connections
Differential geometry of geodesic spheres.
Discrétisation de zeta-déterminants d’opérateurs de Schrödinger sur le tore
Nous donnons ici deux résultats sur le déterminant -régularisé d’un opérateur de Schrödinger sur une variété compacte . Nous construisons, pour , une suite où est un graphe fini qui se plonge dans via de telle manière que soit une triangulation de et où est un laplacien discret sur tel que pour tout potentiel sur , la suite de réels converge après renormalisation vers . Enfin, nous donnons sur toute variété riemannienne compacte de dimension inférieure ou égale à ...
Einstein-Hermitian and anti-Hermitian 4-manifolds
We study 4-dimensional Einstein-Hermitian non-Kähler manifolds admitting a certain anti-Hermitian structure. We also describe Einstein 4-manifolds which are of cohomogeneity 1 with respect to an at least 4-dimensional group of isometries.
Equivalence of Lagrangian germs in the presence of a surface
Erratum: Geometry of the Rolling Ellipsoid
Extended Derdziński-Shen theorem for curvature tensors
We extend a remarkable theorem of Derdziński and Shen, on the restrictions imposed on the Riemann tensor by the existence of a nontrivial Codazzi tensor. We show that the Codazzi equation can be replaced by a more general algebraic condition. The resulting extension applies both to the Riemann tensor and to generalized curvature tensors.
Geometry of the rolling ellipsoid
We study rolling maps of the Euclidean ellipsoid, rolling upon its affine tangent space at a point. Driven by the geometry of rolling maps, we find a simple formula for the angular velocity of the rolling ellipsoid along any piecewise smooth curve in terms of the Gauss map. This result is then generalised to rolling any smooth hyper-surface. On the way, we derive a formula for the Gaussian curvature of an ellipsoid which has an elementary proof and has been previously known only for dimension two....
Global Gronwall estimates for integral curves on Riemannian manifolds.
We prove Gronwall-type estimates for the distance of integral curves of smooth vector fields on a Riemannian manifold. Such estimates are of central importance for all methods of solving ODEs in a verified way, i.e., with full control of roundoff errors. Our results may therefore be seen as a prerequisite for the generalization of such methods to the setting of Riemannian manifolds.
Homogénéité locale pour les métriques riemanniennes holomorphes en dimension
Une métrique riemannienne holomorphe sur une variété complexe est une section holomorphe du fibré des formes quadratiques complexes sur l’espace tangent holomorphe à telle que, en tout point de , la forme quadratique complexe est non dégénérée (de rang maximal, égal à la dimension complexe de ). Il s’agit de l’analogue, dans le contexte holomorphe, d’une métrique riemannienne (réelle). Contrairement au cas réel, l’existence d’une telle métrique sur une variété complexe compacte n’est...
Manifolds with quadratic curvature decay and slow volume growth
Margulis Lemma, entropy and free products
We prove a Margulis’ Lemma à la Besson-Courtois-Gallot, for manifolds whose fundamental group is a nontrivial free product , without 2-torsion. Moreover, if is torsion-free we give a lower bound for the homotopy systole in terms of upper bounds on the diameter and the volume-entropy. We also provide examples and counterexamples showing the optimality of our assumption. Finally we give two applications of this result: a finiteness theorem and a volume estimate for reducible manifolds.
Mean and scalar curvature homogeneous Riemannian manifolds.
Métriques riemanniennes holomorphes en petite dimension
Nous étudions les métriques riemanniennes holomorphes sur les variétés complexes compactes de dimension . Nous montrons que, contrairement au cas réel, une métrique riemannienne holomorphe possède un “grand” pseudo-groupe d’isométries locales. Ceci implique qu’une telle métrique n’existe pas sur les variétés complexes compactes simplement connexes de dimension .
O geometrii laplasiánu. I
O geometrii laplasiánu. II
On a quasilinear elliptic equation and a Riemannian metric invariant under Möbius transformations.
On a quasilinear elliptic equation and a Riemannian metric invariant under Möbius transformations. (Summary).
On holomorphically projective mappings from manifolds with equiaffine connection onto Kähler manifolds
In this paper we study fundamental equations of holomorphically projective mappings from manifolds with equiaffine connection onto (pseudo-) Kähler manifolds with respect to the smoothness class of connection and metrics. We show that holomorphically projective mappings preserve the smoothness class of connections and metrics.
On holomorphically projective mappings of -Kähler manifolds
In this paper we study fundamental equations of holomorphically projective mappings of -Kähler spaces (i.e. classical, pseudo- and hyperbolic Kähler spaces) with respect to the smoothness class of metrics. We show that holomorphically projective mappings preserve the smoothness class of metrics.