Differential Geometry: Cartan's Generalization of Klein's Erlangen Program

By R. Sharpe, S. Chern. 2000

719 citations recorded by the source corpus.

How researchers see this paper

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Gauge Equivariant Convolutional Networks and the Icosahedral CNN (2019, neutral): “For further study, we recommend (Sharpe, 1997; Shoshichi Kobayashi, 1963; Husem¨oller, 1994; Steenrod, 1951; Wendl, 2008; Marsh, 2016; Crane, 2014).”
A General Theory of Equivariant CNNs on Homogeneous Spaces (2018, neutral): “For mathematical background, we recommend [13, 33–37].”
MacDowell–Mansouri gravity and Cartan geometry (2006, methodology): “This path is independent of the lifting γ , depending only on the path in the base manifold M [20].”
Geometric structures as deformed infinitesimal symmetries (2004, background): “6 and 7.”
Differential Geometry and Lie Groups (2020, background): “For yet a notion of submanifold intermediate between immersed submanifolds and (our) submanifolds, see Sharpe [107] (Chapter 1).”
Discrete differential forms for computational modeling (2005, background): “In fact, Sharpe states in [37] that every differential equation may be expressed in term of the exterior derivative of differential forms.”
Elie Cartan's torsion in geometry and in field theory, an essay (2007, background): “…studied by Schweizer et al. [92], Nitsch and Hehl [69], Meyer [61], and more recent advances can be found in Aldrovandi andPereira [1], Andrade and Pereira [2], Gronwald [23], Itin [42, 43], Maluf and da Rocha-Neto [56], Muench [65], Obukhov and Pereira [72], and Schucking ad Surowitz [90, 91].”