Gradient-Like and Integrable Vector Fields on IR2.
Let be a Lagrangian submanifold of for some closed manifold X. Let be a generating function for which is quadratic at infinity, and let W(x) be the corresponding graph selector for in the sense of Chaperon-Sikorav-Viterbo, so that there exists a subset of measure zero such that W is Lipschitz continuous on X, smooth on and for Let H(x,p)=0 for . Then W is a classical solution to on and extends to a Lipschitz function on the whole of X. Viterbo refers to W as a variational...
Some results in the geometry of four-parametric manifolds of three-dimensional spaces in the projective space are found. The properties of such a manifold with characteristics consisting of a quadric and two planes are studied. The properties of the manifold dual to are found. Some results in the geometry of linear spaces from [1],[2],[3],[4] are used. The notation of the quantities is the same as in [4].
We consider a mirror symmetry of simple elliptic singularities. In particular, we construct isomorphisms of Frobenius manifolds among the one from the Gromov–Witten theory of a weighted projective line, the one from the theory of primitive forms for a universal unfolding of a simple elliptic singularity and the one from the invariant theory for an elliptic Weyl group. As a consequence, we give a geometric interpretation of the Fourier coefficients of an eta product considered by K. Saito.
Dans cet article, nous étudions les propriétés asymptotiques d’une large classe de sous-groupe discrets du groupe linéaire réel : les groupes de Ping-Pong. Nous décrivons leur action sur l’espace projectif réel et le comportement à l’infini de leur fonction de comptage.
Soient un espace symétrique de type non compact et un groupe discret d’isométries de du type de Schottky. Dans cet article, nous donnons des équivalents des fonctions orbitales de comptage pour l’action de sur .
Nous considérons une famille de groupes libres et discrets d’isométries orientées agissant sur la boule hyperbolique et contenant des transformations paraboliques; nous démontrons que le nombre de géodésiques fermées de de longueur au plus est équivalent à , où désigne l’exposant critique de la série de Poincaré.
We propose a definition of a Riemannian groupoid, and we show that the Stefan foliation that it induces is a Riemannian (singular) foliation. We also prove that the homotopy groupoid of a Riemannian (regular) foliation is a Riemannian groupoid.