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This ebook is the 1st to give an outline of higher-order Hamilton geometry with purposes to higher-order Hamiltonian mechanics. it's a direct continuation of the publication The Geometry of Hamilton and Lagrange areas, (Kluwer educational Publishers, 2001). It comprises the overall conception of upper order Hamilton areas H(k)n, k>=1, semisprays, the canonical nonlinear connection, the N-linear metrical connection and their constitution equations, and the Riemannian virtually touch metrical version of those areas.

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. E C, zero '1 . be the O-dimensional Lie n crew generated by way of the transformation z ~ >. z, z E C - {a}. Then (cf.

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Modern examine in algebraic geometry is the focal point of this assortment, which offers articles on glossy points of the topic. The record of subject matters coated is a roll-call of a few of crucial and lively issues during this thriving quarter of arithmetic: the reader will locate articles on birational geometry, vanishing theorems, advanced geometry and Hodge concept, loose resolutions and syzygies, derived different types, invariant conception, moduli areas, and similar subject matters, all written by way of best specialists.