Differential and Geometric Structure for the Tangent Bundle of a Projective Limit Manifold
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چکیده
The tangent bundle of a wide class of Fréchet manifolds is studied here. A vector bundle structure is obtained with structural group a topological subgroup of the general linear group of the fiber type. Moreover, basic geometric results, known form the classical case of finite dimensional manifolds, are recovered here: Connections can be defined and are characterized by a generalized type of Christoffel symbols while, at the same time, parallel displacements of curves are possible despite the problems concerning differential equations in Fréchet spaces.
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تاریخ انتشار 2005