Parabolic Geometries I PDF Download
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Author: Andreas Cap
Publisher: American Mathematical Soc.
ISBN: 0821826816
Category : Mathematics
Languages : en
Pages : 643
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Book Description
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.
Author: Andreas Cap
Publisher: American Mathematical Soc.
ISBN: 0821826816
Category : Mathematics
Languages : en
Pages : 643
Get Book
Book Description
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.
Author: Andreas Cap
Publisher: American Mathematical Society(RI)
ISBN: 9781470413811
Category : Conformal geometry
Languages : en
Pages : 643
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Book Description
Author: Andreas Čap
Publisher: American Mathematical Soc.
ISBN: 9780821875353
Category :
Languages : en
Pages :
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Book Description
Author: Ben Chow
Publisher: CRC Press
ISBN: 1439864519
Category : Mathematics
Languages : en
Pages : 216
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Book Description
This book documents the results of a workshop held at the Geometry Center (University of Minnesota, Minneapolis) and captures the excitement of the week.
Author: Vladimir V. Kisil
Publisher: World Scientific
ISBN: 1848168586
Category : Mathematics
Languages : en
Pages : 207
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Book Description
This book is a unique exposition of rich and inspiring geometries associated with Möbius transformations of the hypercomplex plane. The presentation is self-contained and based on the structural properties of the group SL2(R). Starting from elementary facts in group theory, the author unveils surprising new results about the geometry of circles, parabolas and hyperbolas, using an approach based on the Erlangen programme of F Klein, who defined geometry as a study of invariants under a transitive group action.The treatment of elliptic, parabolic and hyperbolic Möbius transformations is provided in a uniform way. This is possible due to an appropriate usage of complex, dual and double numbers which represent all non-isomorphic commutative associative two-dimensional algebras with unit. The hypercomplex numbers are in perfect correspondence with the three types of geometries concerned. Furthermore, connections with the physics of Minkowski and Galilean space-time are considered.
Author: Vladimir V Kisil
Publisher: World Scientific
ISBN: 1908977604
Category : Mathematics
Languages : en
Pages : 208
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Book Description
This book is a unique exposition of rich and inspiring geometries associated with Möbius transformations of the hypercomplex plane. The presentation is self-contained and based on the structural properties of the group SL2(R). Starting from elementary facts in group theory, the author unveils surprising new results about the geometry of circles, parabolas and hyperbolas, using an approach based on the Erlangen programme of F Klein, who defined geometry as a study of invariants under a transitive group action.The treatment of elliptic, parabolic and hyperbolic Möbius transformations is provided in a uniform way. This is possible due to an appropriate usage of complex, dual and double numbers which represent all non-isomorphic commutative associative two-dimensional algebras with unit. The hypercomplex numbers are in perfect correspondence with the three types of geometries concerned. Furthermore, connections with the physics of Minkowski and Galilean space-time are considered./a
Author: Thomas Andrew Ivey
Publisher: American Mathematical Soc.
ISBN: 0821833758
Category : Mathematics
Languages : en
Pages : 394
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Book Description
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.
Author: Rolando Magnanini
Publisher: Springer Science & Business Media
ISBN: 8847028418
Category : Mathematics
Languages : en
Pages : 294
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Book Description
The study of qualitative aspects of PDE's has always attracted much attention from the early beginnings. More recently, once basic issues about PDE's, such as existence, uniqueness and stability of solutions, have been understood quite well, research on topological and/or geometric properties of their solutions has become more intense. The study of these issues is attracting the interest of an increasing number of researchers and is now a broad and well-established research area, with contributions that often come from experts from disparate areas of mathematics, such as differential and convex geometry, functional analysis, calculus of variations, mathematical physics, to name a few. This volume collects a selection of original results and informative surveys by a group of international specialists in the field, analyzes new trends and techniques and aims at promoting scientific collaboration and stimulating future developments and perspectives in this very active area of research.
Author: Filippo Gazzola
Publisher: Springer
ISBN: 3319415387
Category : Mathematics
Languages : en
Pages : 288
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Book Description
This book collects recent research papers by respected specialists in the field. It presents advances in the field of geometric properties for parabolic and elliptic partial differential equations, an area that has always attracted great attention. It settles the basic issues (existence, uniqueness, stability and regularity of solutions of initial/boundary value problems) before focusing on the topological and/or geometric aspects. These topics interact with many other areas of research and rely on a wide range of mathematical tools and techniques, both analytic and geometric. The Italian and Japanese mathematical schools have a long history of research on PDEs and have numerous active groups collaborating in the study of the geometric properties of their solutions.
Author: Frank Morley
Publisher: Courier Corporation
ISBN: 0486493393
Category : Mathematics
Languages : en
Pages : 292
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Book Description
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.
