Titlebook: Gauge Field Theory and Complex Geometry; Yuri Ivanovich Manin Book 1997Latest edition Springer-Verlag Berlin Heidelberg 1997 Kohomologie.Q

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The Radon-Penrose Transform,ometrical structures: complex space-time, with its curvature encoded in the spinor decomposition of the tangent sheaf; fields as sections and connections; and finally, the Lagrangians and the dynamic equations that follow from them. The reader should supplement our brief presentation with more tradi

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Introduction to Supergeometry,on of superspaces and their mappings is given in terms of sheaves. This chapter is devoted to the exposition of the basic facts about superspaces. In § 1 the fundamental definitions are introduced, especially the concept of a supermanifold, a space with local systems of independent coordinate functi

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Geometric Structures of Supersymmetry and Gravitation,. is described. If one begins with twistors, then the compact complex version of . is naturally realized as a flag space. The geometry of the flat case corresponding to the minimal number (. 1) of odd coordinates, after a suitable twist, turns into the geometry of simple gravity according to Ogievet

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Ausbreitungsvorg?nge der Gravitationntegrability, including the Frobenius theorem and connections. In § 5 objects specific to supergeometry are introduced—integral forms. The complex of integral forms is constructed using a canonical right connection on the sheaf of Berezin volume forms of the supermanifold; the idea of a right connec

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Inspirationen von Organisationsexperten, supersymmetric Yang-Mills equations using the Penrose transform in supergeometry; the coordinate computations relating to this are carried out in § 5. In § 6 we classify the other flag superspaces whose underlying space is the Penrose model. They have several exotic properties, but they can be usef

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Introduction to Supergeometry,ntegrability, including the Frobenius theorem and connections. In § 5 objects specific to supergeometry are introduced—integral forms. The complex of integral forms is constructed using a canonical right connection on the sheaf of Berezin volume forms of the supermanifold; the idea of a right connec

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