Titlebook: Introduction to Geometry of Manifolds with Symmetry; V. V. Trofimov Book 1994 Springer Science+Business Media Dordrecht 1994 Algebraic str

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V. V. Trofimov, and its pathophysiology is poorly understood. Moreover, the last two decades have witnessed a dramatic revision of the long-held view of MS as an inflammatory demyelinating white matter disease. Instead, it is now regarded as a global central nervous system (CNS) disorder with a neurodegenerative

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Elements of Differential Geometry, the properties which are preserved under deformations that do not tear or glue together parts of the figure. Thus, the circumference, the boundary of a square, and the knot in Figure 1 have the same topological properties, while the sphere and the surface of a bread-ring have different topological

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Lie Groups and Lie Algebras,hese objects are called . provided that the group operations are smooth. As a rule, Lie groups that occur in applications have nontrivial topological structure. In the introduction to this chapter we will consider one such example, the group SO(3) of orthogonal matrices of size 3 × 3 with the determ

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Symmetric Spaces,is a geodesic with γ(0) = ., then ..(.) = (−.). Such manifolds are called .. The existence of the isometries imposes strong constraints on the structure of the manifolds. For example, . must be ., which means that for any two points .., .. of . there is an isometry . of . that takes .. to ... In ord

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preservative

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