Conformally Osserman Lorentzian manifolds
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-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...
Connection metrics of nonnegative curvature on vector bundles.
Connection theory on differentiable fibre bundles: A concise introduction.
Connections and 1-jet fiber bundles
Connections and applications of some tangency relation of sets.
Connections and regularity on the tangent and cotangent bundle.
Connections in 2-fibered manifolds
Connections in associated fibre bundles
Connections in -vector bundles.
Connections in regular Poisson manifolds over ℝ-Lie foliations
The subject of this paper is the notion of the connection in a regular Poisson manifold M, defined as a splitting of the Atiyah sequence of its Lie algebroid. In the case when the characteristic foliation F is an ℝ-Lie foliation, the fibre integral operator along the adjoint bundle is used to define the Euler class of the Poisson manifold M. When M is oriented 3-dimensional, the notion of the index of a local flat connection with singularities along a closed transversal is defined. If, additionally,...
Connections induced by -tensor fields on cotangent bundles
On cotangent bundles the Liouville field, the Liouville 1-form and the canonical symplectic structure d exist. In this paper interactions between these objects and -tensor fields on cotangent bundles are studied. Properties of the connections induced by the above structures are investigated.
Connections of higher order and product preserving functors
In this paper we consider a product preserving functor of order and a connection of order on a manifold . We introduce horizontal lifts of tensor fields and linear connections from to with respect to . Our definitions and results generalize the particular cases of the tangent bundle and the tangent bundle of higher order.
Connections on 1-jets principal fiber bundles
Connections on distributional bundles