Titlebook: Differential Geometry and Lie Groups; A Computational Pers Jean Gallier,Jocelyn Quaintance Textbook 2020 Springer Nature Switzerland AG 202

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Groups and Group Actionstroduces the concept of a group acting on a set, and defines the Grassmannians and Stiefel manifolds as homogenous manifolds arising from group actions of Lie groups. The last section provides an overview of topological groups, of which Lie groups are a special example, and contains more advanced material that may be skipped upon first reading.

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Basic Analysis: Review of Series and Derivativesperties of power series involving matrix coefficients and a review of the notion of the . of a function between two normed vector spaces. Those readers familiar with these concepts may proceed directly to Chapter ..

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Geodesics on Riemannian Manifolds the structure of a metric space on ., where .(., .) is the greatest lower bound of the length of all curves joining . and .. Curves on . which locally yield the shortest distance between two points are of great interest. These curves, called ., play an important role and the goal of this chapter is to study some of their properties.

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Ratgeber Polyneuropathie und Restless LegsThe purpose of this chapter and the next two chapters is to give a “gentle” and fairly concrete introduction to manifolds, Lie groups, and Lie algebras, our main objects of study.

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Rating Scales for Somatic Disorders,In this chapter we study a class of linear Lie groups known as the Lorentz groups. As we will see, the Lorentz groups provide interesting examples of homogeneous spaces. Moreover, the Lorentz group .(3, 1) shows up in an interesting way in computer vision.

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