Exterior Differential Systems and Euler-Lagrange Partial Differential Equations
by R. Bryant, P. Griffiths, D. Grossman
Publisher: University Of Chicago Press 2008
Number of pages: 219
The authors present the results of their ongoing development of a theory of the geometry of differential equations, focusing especially on Lagrangians and Poincaré-Cartan forms. They also cover certain aspects of the theory of exterior differential systems, which provides the language and techniques for the entire study.
Home page url
Download or read it online for free here:
by Joseph M. Landsberg - arXiv
Homogeneous varieties, Topology and consequences Projective differential invariants, Varieties with degenerate Gauss images, Dual varieties, Linear systems of bounded and constant rank, Secant and tangential varieties, and more.
by Stefan Waldmann - arXiv
We discuss the solution theory of geometric wave equations as they arise in Lorentzian geometry: for a normally hyperbolic differential operator the existence and uniqueness properties of Green functions and Green operators is discussed.
by J.L. Koszul - Tata Institute of Fundamental Research
From the table of contents: Differential Calculus; Differentiable Bundles; Connections on Principal Bundles; Holonomy Groups; Vector Bundles and Derivation Laws; Holomorphic Connections (Complex vector bundles, Almost complex manifolds, etc.).
by Bianca Santoro - arXiv
The author aimed at providing a first introduction to the main general ideas on the study of the Ricci flow, as well as guiding the reader through the steps of Kaehler geometry for the understanding of the complex version of the Ricci flow.