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

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書目名稱Differential Geometry and Lie Groups影響因子(影響力)




書目名稱Differential Geometry and Lie Groups影響因子(影響力)學(xué)科排名




書目名稱Differential Geometry and Lie Groups網(wǎng)絡(luò)公開度




書目名稱Differential Geometry and Lie Groups網(wǎng)絡(luò)公開度學(xué)科排名




書目名稱Differential Geometry and Lie Groups被引頻次




書目名稱Differential Geometry and Lie Groups被引頻次學(xué)科排名




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書目名稱Differential Geometry and Lie Groups年度引用學(xué)科排名




書目名稱Differential Geometry and Lie Groups讀者反饋




書目名稱Differential Geometry and Lie Groups讀者反饋學(xué)科排名

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Introduction to Manifolds and Lie Groupsial structure, which means that the notion of tangent space makes sense at any point of the group. Furthermore, the tangent space at the identity happens to have some algebraic structure, that of a Lie algebra. Roughly speaking, the tangent space at the identity provides a “l(fā)inearization” of the Lie

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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 ma

平庸的人或物

Manifolds, Tangent Spaces, Cotangent Spaces, and Submanifoldsifolds, it is necessary to generalize the concept of a manifold to spaces that are not a priori embedded in some .. The basic idea is still that whatever a manifold is, it is a topological space that can be covered by a collection of open subsets .., where each .. is isomorphic to some “standard mod

CLAM

Construction of Manifolds from Gluing Data ,ome indirect information about the overlap of the domains .. of the local charts defining our manifold . in terms of the transition functions . but where . itself is not known. For example, this situation happens when trying to construct a surface approximating a 3D-mesh. If we let Ω.?=?..(..?∩?..)a

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不妥協(xié)

Riemannian Metrics and Riemannian Manifoldsfold. The idea is to equip the tangent space .. at . to the manifold . with an inner product 〈?, ?〉., in such a way that these inner products vary smoothly as . varies on .. It is then possible to define the length of a curve segment on a . and to define the distance between two points on ..

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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

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