EuDML | Browse

For a riemannian structure on a semidirect product of Lie groups, the variational problems can be reduced using the group symmetry. Choosing the Levi-Civita connection of a positive definite metric tensor, instead of any of the canonical connections for the Lie group, simplifies the reduction of the variations but complicates the expression for the Lie algebra valued covariant derivatives. The origin of the discrepancy is in the semidirect product structure, which implies that the riemannian exponential...

Reduction by group symmetry of second order variational problems on a semidirect product of Lie groups with positive definite Riemannian metric

Claudio Altafini (2010)

ESAIM: Control, Optimisation and Calculus of Variations

For a Riemannian structure on a semidirect product of Lie groups, the variational problems can be reduced using the group symmetry. Choosing the Levi-Civita connection of a positive definite metric tensor, instead of any of the canonical connections for the Lie group, simplifies the reduction of the variations but complicates the expression for the Lie algebra valued covariant derivatives. The origin of the discrepancy is in the semidirect product structure, which implies that the Riemannian exponential...

Representation of a gauge group as motions of a Hilbert space

Clara Lucía Aldana Domínguez (2004)

Annales mathématiques Blaise Pascal

This is a survey article based on the author’s Master thesis on affine representations of a gauge group. Most of the results presented here are well-known to differential geometers and physicists familiar with gauge theory. However, we hope this short systematic presentation offers a useful self-contained introduction to the subject.In the first part we present the construction of the group of motions of a Hilbert space and we explain the way in which it can be considered as a Lie group. The second...

Representations of the group of functions taking values in a compact Lie group

I. M. Gelfand, M. I. Graev, A. M. Veršik (1980)

Compositio Mathematica

Riemannian geometries on spaces of plane curves

Peter W. Michor, David Mumford (2006)

Journal of the European Mathematical Society

We study some Riemannian metrics on the space of smooth regular curves in the plane, viewed as the orbit space of maps from $S^{1}$ to the plane modulo the group of diffeomorphisms of $S^{1}$ , acting as reparametrizations. In particular we investigate the metric, for a constant $A > 0$ , $G_{c}^{A} (h, k) : = \int_{S^{1}} (1 + A κ_{c} {(θ)}^{2}) 〈 h (θ), k (θ) 〉 | c^{'} (θ) | d θ$ where $κ_{c}$ is the curvature of the curve $c$ and $h$ , $k$ are normal vector fields to $c$ . The term $A κ^{2}$ is a sort of geometric Tikhonov regularization because, for $A = 0$ , the geodesic distance between any two distinct curves is 0, while for $A > 0$ the...

Rigidité de quelques groupes de germes de difféomorphismes.

Frédéric Touzet (2003)

Publicacions Matemàtiques

Using the description of non solvable dynamics by Nakai, we give in this paper a new proof of the rigidity properties of some sub-groups of Diff(C, O). The Cinfinity case is also considered here.

Rigidity of group actions

Masahiko Kanai (1996/1997)

Séminaire de théorie spectrale et géométrie

Rigidity of integral curves of rank 2 distributions.

Robert L. Bryant, Lucas Hsu (1993)

Inventiones mathematicae

Schwarzian derivative related to modules of differential operators on a locally projective manifold

S. Bouarroudj, V. Ovsienko (2000)

Banach Center Publications

We introduce a 1-cocycle on the group of diffeomorphisms Diff(M) of a smooth manifold M endowed with a projective connection. This cocycle represents a nontrivial cohomology class of Diff(M) related to the Diff(M)-modules of second order linear differential operators on M. In the one-dimensional case, this cocycle coincides with the Schwarzian derivative, while, in the multi-dimensional case, it represents its natural and new generalization. This work is a continuation of [3] where the same problems...

Second cohomology classes of the group of $C^{1}$ -flat diffeomorphisms

Tomohiko Ishida (2012)

Annales de l’institut Fourier

We study the cohomology of the group consisting of all $C^{\infty}$ -diffeomorphisms of the line, which are $C^{1}$ -flat to the identity at the origin. We construct non-trivial two second real cohomology classes and uncountably many second integral homology classes of this group.

Self-homeomorphisms of the 2-sphere which fix pointwise a nonseparating continuum

Paul Fabel (1998)

Fundamenta Mathematicae

We prove that the space of orientation preserving homeomorphisms of the 2-sphere which fix pointwise a nontrivial nonseparating continuum is a contractible absolute neighborhood retract homeomorphic to the separable Hilbert space $l_{2}$ .

Singular Yang-Mills connections

Johan Rade (1995)

Journées équations aux dérivées partielles

Singularities and normal forms of generic 2-distributions on 3-manifolds

B. Jakubczyk, M. Zhitomirskiĭ (1995)

Studia Mathematica

We give a complete classification of germs of generic 2-distributions on 3-manifolds. By a 2-distribution we mean either a module generated by two vector fields (at singular points its dimension decreases) or a Pfaff equation, i.e. a module generated by a differential 1-form (at singular points the dimension of its kernel increases).

Currently displaying 281 – 300 of 423

Previous Page 15 Next

Displaying 281 – 300 of 423

Rational evalutation subgroups.

Réarrangements des difféomorphismes sur une variété compacte mesurée

Recent developments in the theory of function spaces

Recognition of $𝒦$ -singularities of functions.

Reduction by group symmetry of second order variational problems on a semidirect product of Lie groups with positive definite riemannian metric