Parabolic Geometries I - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Parabolic Geometries I write by Andreas Čap. This book was released on 2024-07-29. Parabolic Geometries I available in PDF, EPUB and Kindle. Parabolic geometries encompass a very diverse class of geometric structures, including such important examples as conformal, projective, and almost quaternionic structures, hypersurface type CR-structures and various types of generic distributions. The characteristic feature of parabolic geometries is an equivalent description by a Cartan geometry modeled on a generalized flag manifold (the quotient of a semisimple Lie group by a parabolic subgroup). Background on differential geometry, with a view towards Cartan connections, and on semisimple Lie algebras and their representations, which play a crucial role in the theory, is collected in two introductory chapters. The main part discusses the equivalence between Cartan connections and underlying structures, including a complete proof of Kostant's version of the Bott–Borel–Weil theorem, which is used as an important tool. For many examples, the complete description of the geometry and its basic invariants is worked out in detail. The constructions of correspondence spaces and twistor spaces and analogs of the Fefferman construction are presented both in general and in several examples. The last chapter studies Weyl structures, which provide classes of distinguished connections as well as an equivalent description of the Cartan connection in terms of data associated to the underlying geometry. Several applications are discussed throughout the text.
Parabolic Geometries I
Parabolic Geometries I - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Parabolic Geometries I write by Andreas Cap. This book was released on 2009. Parabolic Geometries I available in PDF, EPUB and Kindle. Discusses the equivalence between Cartan connections and underlying structures, including a complete proof of Kostant's version of the Bott - Borel - Weil theorem, which is used as an important tool. This book provides a description of the geometry and its basic invariants.
Cartan for Beginners
Cartan for Beginners - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Cartan for Beginners write by Thomas Andrew Ivey. This book was released on 2003. Cartan for Beginners available in PDF, EPUB and Kindle. This book is an introduction to Cartan's approach to differential geometry. Two central methods in Cartan's geometry are the theory of exterior differential systems and the method of moving frames. This book presents thorough and modern treatments of both subjects, including their applications to both classic and contemporary problems. It begins with the classical geometry of surfaces and basic Riemannian geometry in the language of moving frames, along with an elementary introduction to exterior differential systems. Key concepts are developed incrementally with motivating examples leading to definitions, theorems, and proofs. Once the basics of the methods are established, the authors develop applications and advanced topics.One notable application is to complex algebraic geometry, where they expand and update important results from projective differential geometry. The book features an introduction to $G$-structures and a treatment of the theory of connections. The Cartan machinery is also applied to obtain explicit solutions of PDEs via Darboux's method, the method of characteristics, and Cartan's method of equivalence. This text is suitable for a one-year graduate course in differential geometry, and parts of it can be used for a one-semester course. It has numerous exercises and examples throughout. It will also be useful to experts in areas such as PDEs and algebraic geometry who want to learn how moving frames and exterior differential systems apply to their fields.
Inversive Geometry
Inversive Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Inversive Geometry write by Frank Morley. This book was released on 2014-01-15. Inversive Geometry available in PDF, EPUB and Kindle. This introduction to algebraic geometry makes particular reference to the operation of inversion. Topics include Euclidean group; inversion; quadratics; finite inversive groups; parabolic, hyperbolic, and elliptic geometries; differential geometry; and more. 1933 edition.
Geometric Theory of Semilinear Parabolic Equations
Geometric Theory of Semilinear Parabolic Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Theory of Semilinear Parabolic Equations write by Daniel Henry. This book was released on 2006-11-15. Geometric Theory of Semilinear Parabolic Equations available in PDF, EPUB and Kindle.
