Add to ORKGIn this thesis we investigate some geometric properties of the contactomorphism group Dθ(M) of a compact, oriented, contact manifold of odd dimension. We endow this group with two different weak Riemannain metrics, the L2 and the H1, and investigate properties such as curvature, geodesic flows, conjugate points, and exponential maps. This group has applications to fluid mechanics as it is the natural generalization to D(S1), the diffeomorphism group of the circle, which is already a heavily studied object. We end with providing numerical evidence that the sectional curvature of the group D(S1)/S1, the diffeomorphism group of the circle modulo its rotations, given the H1/2 metric is non-negative. We leave the proof, or search for counterexa...
In this paper we are concerned with the manifold structure of certain groups of diffeomorphisms, and...
For a closed connected manifold N, we establish the existence of geometric structures on various sub...
In this article, we propose a group model G of a real extension of the Lobachevsky plane H2 × R . Th...
The topological group D-k(S) of diffeomorphisms of the unit circle 5 of Sobolev class H-k, for k lar...
the group of diffeomorphisms 3) of a compact «-manifold M, possibly with boundary. The group 3D has ...
Abstract. For a compact contact manifold M2n+1, it is shown that the anisotropic Folland-Stein funct...
AbstractHolm, Marsden, and Ratiu (Adv. in Math.137(1998), 1–81) derived a new model for the mean mot...
This paper develops the geometric analysis of geodesic flow of a new right invariant metric {.,.}_1 ...
summary:The study of diffeomorphism group actions requires methods of infinite dimensional analysis....
We first describe the action of the fundamental group of a closed surface of variable negative curva...
For a closed connected manifold N, we establish the existence of geometric structures on various sub...
In dieser Arbeit werden die Beziehungen zwischen Lorentzgeometrie und Kontaktgeometrie untersucht. I...
We establish the existence of three new subgroups of the group of volume-preserving diffeomorphisms ...
We show that certain right-invariant metrics endow the infinite-dimensional Lie group of all smooth ...
International audienceThe geodesic equations of a class of right invariant metrics on the semi-direc...
In this paper we are concerned with the manifold structure of certain groups of diffeomorphisms, and...
For a closed connected manifold N, we establish the existence of geometric structures on various sub...
In this article, we propose a group model G of a real extension of the Lobachevsky plane H2 × R . Th...
The topological group D-k(S) of diffeomorphisms of the unit circle 5 of Sobolev class H-k, for k lar...
the group of diffeomorphisms 3) of a compact «-manifold M, possibly with boundary. The group 3D has ...
Abstract. For a compact contact manifold M2n+1, it is shown that the anisotropic Folland-Stein funct...
AbstractHolm, Marsden, and Ratiu (Adv. in Math.137(1998), 1–81) derived a new model for the mean mot...
This paper develops the geometric analysis of geodesic flow of a new right invariant metric {.,.}_1 ...
summary:The study of diffeomorphism group actions requires methods of infinite dimensional analysis....
We first describe the action of the fundamental group of a closed surface of variable negative curva...
For a closed connected manifold N, we establish the existence of geometric structures on various sub...
In dieser Arbeit werden die Beziehungen zwischen Lorentzgeometrie und Kontaktgeometrie untersucht. I...
We establish the existence of three new subgroups of the group of volume-preserving diffeomorphisms ...
We show that certain right-invariant metrics endow the infinite-dimensional Lie group of all smooth ...
International audienceThe geodesic equations of a class of right invariant metrics on the semi-direc...
In this paper we are concerned with the manifold structure of certain groups of diffeomorphisms, and...
For a closed connected manifold N, we establish the existence of geometric structures on various sub...
In this article, we propose a group model G of a real extension of the Lobachevsky plane H2 × R . Th...