Topic
Klein geometry
About: Klein geometry is a research topic. Over the lifetime, 64 publications have been published within this topic receiving 1700 citations.
Papers published on a yearly basis
Papers
Book•
21 Nov 2000
TL;DR: In the Ashes of the Ether: Differential Topology, Looking for the Forest in the Leaves: Folations, The Fundamental Theorem of Calculus and Shapes Fantastic: Klein Geometries as mentioned in this paper.
Abstract: In the Ashes of the Ether: Differential Topology.- Looking for the Forest in the Leaves: Folations.- The Fundamental Theorem of Calculus.- Shapes Fantastic: Klein Geometries.- Shapes High Fantastical: Cartan Geometries.- Riemannian Geometry.- Mobius Geometry.- Projective Geometry.- Appendix A - E.
506 citations
258 citations
Book•
20 Oct 2003TL;DR: Lie groups Maximal tori and the classification theorem The geometry of a compact Lie group Homogeneous spaces as mentioned in this paper and the geometry of reductive homogeneous spaces Symmetric spaces Generalized flag manifolds Advanced topics Bibliography Index
Abstract: Lie groups Maximal tori and the classification theorem The geometry of a compact Lie group Homogeneous spaces The geometry of a reductive homogeneous space Symmetric spaces Generalized flag manifolds Advanced topics Bibliography Index.
225 citations
TL;DR: The motion of plane curves in Klein geometry is studied in this paper, where it is shown that the KdV, Harry-Dym, Sawada-Kotera, Burgers, the defocusing mKdV hierarchies, the Camassa-Holm and the Kaup-Kupershmidt equation naturally arise from the motions of planes in SL(2)-, Sim(2), SA(2) and A(2-) geometries.
214 citations
Book•
16 May 1984
TL;DR: Wussing as discussed by the authors traces the process of abstraction that led finally to the axiomatic formulation of the abstract notion of group, and concludes with a sketch of the state of group theory about 1920, when the axiom systems of Webber had been formalized and investigated in their own right.
Abstract: In this book, Hans Wussing sets out to trace the process of abstraction that led finally to the axiomatic formulation of the abstract notion of group. His main thesis is that the roots of the abstract notion of group do not lie, as frequently assumed, only in the theory of algebraic equations; they are also to be found in the geometry and the theory of numbers of the end of the 18th and the first half of the 19th centuries.The book takes us from Lagrange via Cauchy, Abel, and Galois to Serret and Camille Jordan. It then turns to Cayley, to Felix Klein's Erlangen Program, and to Sophus Lie, and ends with a sketch of the state of group theory about 1920, when the axiom systems of Webber had been formalized and investigated in their own right.
100 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2018 | 1 |
| 2017 | 3 |
| 2015 | 2 |
| 2014 | 2 |
| 2013 | 1 |
| 2012 | 2 |