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Cartan for beginners
Thomas A. Ivey,Joseph M. Landsberg +1 more
- 01 Jan 2003
289
TL;DR: In this article, Cartan-Kahler et al. present the Cartan algorithm for linear Pfaffian systems for moving frames and exterior differential systems in projective geometry.
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Abstract: Moving frames and exterior differential systems Euclidean geometry and Riemannian geometry Projective geometry Cartan-Kahler I: Linear algebra and constant-coefficient homogeneous systems Cartan-Kahler II: The Cartan algorithm for linear Pfaffian systems Applications to PDE Cartan-Kahler III: The general case Geometric structures and connections Linear algebra and representation theory Differential forms Complex structures and complex manifolds Initial value problems Hints and answers to selected exercises Bibliography Index
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Citations
•Book
Modular forms, a computational approach
William Stein
- 01 Jan 2007
TL;DR: Modular forms Modular forms of level $1$ Modular form of weight $2$ Dirichlet characters Eisenstein series and Bernoulli numbers Dimension formulas Linear algebra General modular symbols Computing with new forms Computing periods Solutions to selected exercises Appendix A: Computing in higher rank Bibliography Index.
Singularities of improper affine spheres and surfaces of constant Gaussian curvature
Goo Ishikawa,Yoshinori Machida +1 more
TL;DR: In this article, the authors studied the singularities appearing in geometric solutions to the affine affine sphere equation and provided the generic classification of singularities in the solution as well as their duals for surfaces of constant Gaussian curvature.
Framed Surfaces in the Euclidean Space
Tomonori Fukunaga,Masatomo Takahashi +1 more
- 01 Mar 2019
TL;DR: In this paper, the basic invariants and curvatures of a smooth surface with a moving frame are introduced, and the existence and uniqueness of the fundamental invariants of the framed surfaces are established.
48
A Geometric Theory of Nonlinear Morphoelastic Shells
TL;DR: A general geometric theory of nonlinear morphoelastic shells is formulated that describes both the evolution of the body shape, viewed as an orientable surface, as well as its intrinsic material properties such as its reference curvatures.
Linear Surface Reconstruction from Discrete Fundamental Forms on Triangle Meshes
TL;DR: A linear algorithm to reconstruct the vertex coordinates for a surface mesh given its edge lengths and dihedral angles, unique up to rotation and translation, which can benefit a wide range of geometry processing tasks such as surface deformation and shape analysis.
References
•Book
Principles of Algebraic Geometry
Phillip Griffiths,Joe Harris +1 more
- 01 Jan 1978
TL;DR: In this paper, a comprehensive, self-contained treatment of complex manifold theory is presented, focusing on results applicable to projective varieties, and including discussion of the theory of Riemann surfaces and algebraic curves, algebraic surfaces and the quadric line complex.
9.1K
•Book
Differential Geometry, Lie Groups, and Symmetric Spaces
Sigurdur Helgason
- 01 Jan 1978
TL;DR: In this article, the structure of semisimplepleasure Lie groups and Lie algebras is studied. But the classification of simple Lie algesbras and of symmetric spaces is left open.
•Book
Introduction to Lie Algebras and Representation Theory
James E. Humphreys
- 23 Jan 1973
TL;DR: In this paper, Semisimple Lie Algebras and root systems are used for representation theory, isomorphism and conjugacy theorem, and existence theorem for representation.
5.9K
•Book
Lie groups beyond an introduction
Anthony W. Knapp
- 01 Jan 1988
TL;DR: In this paper, closed linear groups Lie Algebras and Lie groups are used to represent finite-dimensional representations of Lie groups, and the structure theory of Semisimple Group Advanced Structure Theory Integration Induced Representations and Branching Theorems are discussed.
2.6K
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