Add to ORKGThe vector bundle structure obtained on the second order (acceleration) tangent bundle T^2M of a smooth manifold M by means of a linear connection on the base provides an alternative way for the study of second order differential equations on manifolds of finite and infinite dimension. Second order vector fields and their integral curves provide a new way of solving a wide class of second order differential equations on Frechet manifolds and may be used also to describe geodesic curves on a Riemannian manifold. The new technique proposed is illustrated by concrete examples within the framework of Banach and Frechet spaces as well as on Lie groups
Given a second order differential equation on a manifold we find necessary and sufficient conditions...
AbstractLet M be a differentiable manifold. A vector field Γ of TM which corresponds to a system of ...
Graduation date: 1976A theory of higher order connections is developed as\ud a reduction of the stru...
The vector bundle structure obtained on the second order (acceleration) tangent bundle T^2M of a smo...
On a smooth manifold M, the vector bundle structures of the second order tangent bundle, T^2M biject...
Abstract. On a smooth manifold M, the vector bundle structures of the second order tangent bundle, T...
The second order tangent bundle T^2M of a smooth manifold M consists of the equivalence classes of c...
On a smooth Banach manifold M, the equivalence classes of curves that agree up to acceleration form ...
We consider an infinite dimensional manifold M modelled on a Banach space E and we construct smooth ...
On a smooth Banach manifold M,$the equivalence classes of curves that agree up to acceleration form ...
© 2014, Pleiades Publishing, Ltd. The second order tangent bundle T2M of a smooth manifold M carries...
Working within the framework of Fréchet modelled infinite dimensional manifolds, we propose a genera...
Some recent work in Frechet geometry is briefly reviewed. In particular an earlier result on the str...
Some recent work in Fréchet geometry is briefly reviewed. In particular an earlier result on the st...
summary:The geometry of second-order systems of ordinary differential equations represented by $2$-c...
Given a second order differential equation on a manifold we find necessary and sufficient conditions...
AbstractLet M be a differentiable manifold. A vector field Γ of TM which corresponds to a system of ...
Graduation date: 1976A theory of higher order connections is developed as\ud a reduction of the stru...
The vector bundle structure obtained on the second order (acceleration) tangent bundle T^2M of a smo...
On a smooth manifold M, the vector bundle structures of the second order tangent bundle, T^2M biject...
Abstract. On a smooth manifold M, the vector bundle structures of the second order tangent bundle, T...
The second order tangent bundle T^2M of a smooth manifold M consists of the equivalence classes of c...
On a smooth Banach manifold M, the equivalence classes of curves that agree up to acceleration form ...
We consider an infinite dimensional manifold M modelled on a Banach space E and we construct smooth ...
On a smooth Banach manifold M,$the equivalence classes of curves that agree up to acceleration form ...
© 2014, Pleiades Publishing, Ltd. The second order tangent bundle T2M of a smooth manifold M carries...
Working within the framework of Fréchet modelled infinite dimensional manifolds, we propose a genera...
Some recent work in Frechet geometry is briefly reviewed. In particular an earlier result on the str...
Some recent work in Fréchet geometry is briefly reviewed. In particular an earlier result on the st...
summary:The geometry of second-order systems of ordinary differential equations represented by $2$-c...
Given a second order differential equation on a manifold we find necessary and sufficient conditions...
AbstractLet M be a differentiable manifold. A vector field Γ of TM which corresponds to a system of ...
Graduation date: 1976A theory of higher order connections is developed as\ud a reduction of the stru...