Conformally covariant field equations
Conformally equivariant quantization : existence and uniqueness
We prove the existence and the uniqueness of a conformally equivariant symbol calculus and quantization on any conformally flat pseudo-riemannian manifold . In other words, we establish a canonical isomorphism between the spaces of polynomials on and of differential operators on tensor densities over , both viewed as modules over the Lie algebra where . This quantization exists for generic values of the weights of the tensor densities and we compute the critical values of the weights yielding...
Conformally flat contact metric manifolds with .
Conformally flat Lorentzian three-spaces with various properties of symmetry and homogeneity
We study conformally flat Lorentzian three-manifolds which are either semi-symmetric or pseudo-symmetric. Their complete classification is obtained under hypotheses of local homogeneity and curvature homogeneity. Moreover, examples which are not curvature homogeneous are described.
Conformally flat manifolds, Kleinian groups and scalar curvature.
Conformally flat pseudo-symmetric spaces of constant type
We give the complete classification of conformally flat pseudo-symmetric spaces of constant type.
Conformally flat semi-symmetric spaces
We obtain the complete classification of conformally flat semi-symmetric spaces.
Conformally flat submanifolds
Conformally Flat Submanifolds of Euclidean Space.
Conformally geodesic mappings satisfying a certain initial condition
In this paper we study conformally geodesic mappings between pseudo-Riemannian manifolds and , i.e. mappings satisfying , where are conformal mappings and is a geodesic mapping. Suppose that the initial condition is satisfied at a point and that at this point the conformal Weyl tensor does not vanish. We prove that then is necessarily conformal.
Conformally invariant wave equations in -de Sitter linear gravity
Conformally Osserman Lorentzian manifolds
Conformally symmetric spaces admitting special quadratic first integrals
Congruences of surfaces in
Conic degeneration of the Dirac operator
Conjecture de H. Hopf sur les produits de variétés
Conjugate and cut loci of a two-sphere of revolution with application to optimal control
Conjugate and cut time in the sub-Riemannian problem on the group of motions of a plane
The left-invariant sub-Riemannian problem on the group of motions (rototranslations) of a plane SE(2) is studied. Local and global optimality of extremal trajectories is characterized. Lower and upper bounds on the first conjugate time are proved. The cut time is shown to be equal to the first Maxwell time corresponding to the group of discrete symmetries of the exponential mapping. Optimal synthesis on an open dense subset of the state space is described.
Conjugate Connections and Radon's Theorem in Affine Differential Geometry.
Conjugate-cut loci and injectivity domains on two-spheres of revolution
In a recent article [B. Bonnard, J.-B. Caillau, R. Sinclair and M. Tanaka, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 26 (2009) 1081–1098], we relate the computation of the conjugate and cut loci of a family of metrics on two-spheres of revolution whose polar form is g = dϕ2 + m(ϕ)dθ2 to the period mapping of the ϕ-variable. One purpose of this article is to use this relation to evaluate the cut and conjugate loci for a family of metrics arising as a deformation of the round sphere and to determine...