An Intro. to Differential Geometry With Applns to Elasticity by P. Ciarlet

By P. Ciarlet

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A / Á 1. That is, a is a Reeb vector field of the contact form ˛. , the quotient of U by a sufficiently small neighbourhood of the identity in Ta , is a manifold. Then MU inherits a canonical symplectic structure ! / D d˛ for the canonical projection W U ! MU . It is now our aim to construct a connection on MU which is “naturally” associated to the given structure. For this, we let G0 G be the connected subgroup with Lie algebra g0 Ä g. Since g0 Ä p and hence G0 P , it follows that we have a fibration P =G0 !

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