Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

Special Issue “Élie Cartan and Differential Geometry”

The Guest Editors for this special issue are

Robert Bryant (Duke University and MSRI in Berkeley, USA)
Thomas Ivey (College of Charleston, USA)
Niky Kamran (McGill University, Montreal, Canada)
Joseph Landsberg (Texas A&M University, USA)
Keti Tenenblat (Universidade de Brasília, Brasil)

The impact of the contributions of Élie Cartan (1869–1951) to differential geometry is still strongly felt today, particularly in the areas manifolds with special geometric structures, submanifold geometry and exterior differential systems, and this special issue of SIGMA aims to present some contributions that reflect the central place of Élie Cartan's legacy in contemporary differential geometry.

Possible topics for papers include

  • geometry of manifolds via moving frames;
  • projective differential geometry, both real and complex;
  • conformal geometry;
  • connections and holonomy;
  • equivalence problems;
  • exterior differential systems.
Even though Lie groups are not one of the specific topics covered in the volume, they are a recurring theme throughout the contributions of the volume.

How to Submit an Article to the Issue.

The length of an article is not limited.

Publication will be done only on the results of the peer review according to refereeing policy of SIGMA.

If you have your paper ready earlier than the deadline, we encourage you to send it now. We will start the reviewing process and publish the paper as soon as the positive publication decision is made. The paper will be indexed in the relevant databases as soon as it is published without waiting for completion of the special issue.

Papers in this Issue:

Contact Geometry of Curves
Peter J. Vassiliou
SIGMA 5 (2009), 098, 27 pages   [ abs   pdf   ps ]
Indefinite Affine Hyperspheres Admitting a Pointwise Symmetry. Part 2
Christine Scharlach
SIGMA 5 (2009), 097, 22 pages   [ abs   pdf   ps ]
Geometry of Control-Affine Systems
Jeanne N. Clelland, Christopher G. Moseley and George R. Wilkens
SIGMA 5 (2009), 095, 28 pages   [ abs   pdf   ps ]
On Tanaka's Prolongation Procedure for Filtered Structures of Constant Type
Igor Zelenko
SIGMA 5 (2009), 094, 21 pages   [ abs   pdf   ps ]
Compact Riemannian Manifolds with Homogeneous Geodesics
Dmitrii V. Alekseevsky and Yurii G. Nikonorov
SIGMA 5 (2009), 093, 16 pages   [ abs   pdf   ps ]
Existence and Construction of Vessiot Connections
Dirk Fesser and Werner M. Seiler
SIGMA 5 (2009), 092, 41 pages   [ abs   pdf   ps ]
Variations of Hodge Structure Considered as an Exterior Differential System: Old and New Results
James Carlson, Mark Green and Phillip Griffiths
SIGMA 5 (2009), 087, 40 pages   [ abs   pdf   ps ]
Natural Intrinsic Geometrical Symmetries
Stefan Haesen and Leopold Verstraelen
SIGMA 5 (2009), 086, 15 pages   [ abs   pdf   ps ]
Higher Order Connections
Michael G. Eastwood
SIGMA 5 (2009), 082, 10 pages   [ abs   pdf   ps ]
Conformal Structures Associated to Generic Rank 2 Distributions on 5-Manifolds – Characterization and Killing-Field Decomposition
Matthias Hammerl and Katja Sagerschnig
SIGMA 5 (2009), 081, 29 pages   [ abs   pdf   ps ]
Symmetric Space Cartan Connections and Gravity in Three and Four Dimensions
Derek K. Wise
SIGMA 5 (2009), 080, 18 pages   [ abs   pdf   ps ]
About Twistor Spinors with Zero in Lorentzian Geometry
Felipe Leitner
SIGMA 5 (2009), 079, 12 pages   [ abs   pdf   ps ]
On Spinor Varieties and Their Secants
Laurent Manivel
SIGMA 5 (2009), 078, 22 pages   [ abs   pdf   ps ]
On the Structure of Lie Pseudo-Groups
Peter J. Olver, Juha Pohjanpelto and Francis Valiquette
SIGMA 5 (2009), 077, 14 pages   [ abs   pdf   ps ]
Boundaries of Graphs of Harmonic Functions
Daniel Fox
SIGMA 5 (2009), 068,  8 pages   [ abs   pdf   ps ]
Symplectic Applicability of Lagrangian Surfaces
Emilio Musso and Lorenzo Nicolodi
SIGMA 5 (2009), 067, 18 pages   [ abs   pdf   ps ]
Holonomy and Projective Equivalence in 4-Dimensional Lorentz Manifolds
Graham S. Hall and David P. Lonie
SIGMA 5 (2009), 066, 23 pages   [ abs   pdf   ps ]
Non-Hamiltonian Actions and Lie-Algebra Cohomology of Vector Fields
Roberto Ferreiro Pérez and Jaime Muñoz Masqué
SIGMA 5 (2009), 063,  7 pages   [ abs   pdf   ps ]
Cartan Connections and Lie Algebroids
Michael Crampin
SIGMA 5 (2009), 061, 13 pages   [ abs   pdf   ps ]
Extension Phenomena for Holomorphic Geometric Structures
Benjamin McKay
SIGMA 5 (2009), 058, 45 pages   [ abs   pdf   ps ]
The Explicit Construction of Einstein Finsler Metrics with Non-Constant Flag Curvature
Enli Guo, Xiaohuan Mo and Xianqiang Zhang
SIGMA 5 (2009), 045,  7 pages   [ abs   pdf   ps ]
Einstein Gravity, Lagrange-Finsler Geometry, and Nonsymmetric Metrics
Sergiu I. Vacaru
SIGMA 4 (2008), 071, 29 pages   [ abs   pdf   ps ]
Exterior Differential Systems for Yang-Mills Theories
Frank B. Estabrook
SIGMA 4 (2008), 063,  4 pages   [ abs   pdf   ps ]
Isoparametric and Dupin Hypersurfaces
Thomas E. Cecil
SIGMA 4 (2008), 062, 28 pages   [ abs   pdf   ps ]
Contact Geometry of Hyperbolic Equations of Generic Type
Dennis The
SIGMA 4 (2008), 058, 52 pages   [ abs   pdf   ps ]

Forthcoming papers:

Singularity Classes of Special 2-Flags
Piotr Mormul
Isomorphism of Intransitive Lie Equations
J.M.M. Veloso

Special Issues in SIGMA

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