Titlebook: Bieberbach Groups and Flat Manifolds; Leonard S. Charlap Textbook 1986 Springer-Verlag New York Inc. 1986 Algebraic structure.Finite.Invar

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0172-5939 he entire space, so you can‘t conclude the space is euclidean space itself. In this book we are mainly concerned with compact flat riemannian manifolds, and unl978-0-387-96395-2978-1-4613-8687-2Series ISSN 0172-5939 Series E-ISSN 2191-6675

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0172-5939 on flat riemannian manifolds. On the other hand it attempts to be a textbook which can be used for a second year graduate course. My aim was to keep the second personality dominant, but the reference persona kept breaking out especially at the end of sections in the form of remarks that contain more

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Holonomy Groups of Prime Order,abelian groups, so the only compact riemannian manifolds with trivial holonomy group are the flat tori. Notice that we did not have to say that the riemannian manifold was “flat” since by Theorem 3.2 of Chapter II, any manifold with a finite (or even merely totally disconnected) holonomy group must have zero curvature.

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Textbook 1986emannian manifolds. On the other hand it attempts to be a textbook which can be used for a second year graduate course. My aim was to keep the second personality dominant, but the reference persona kept breaking out especially at the end of sections in the form of remarks that contain more advanced

Gentry

Flat Riemannian Manifolds,n some wonderful results in riemannian geometry which, after a little initial work, come free with the algebraic results on Bieberbach groups. This procedure in which problems in one field, riemannian geometry, are converted to problems in another field, algebra, is very much in the spirit of modern

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Holonomy Groups of Prime Order,t for the holonomy group Φ. It is, of course, trivial to see that the only Bieberbach groups with trivial holonomy groups (i.e. Φ = {1}) are the free abelian groups, so the only compact riemannian manifolds with trivial holonomy group are the flat tori. Notice that we did not have to say that the ri

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