[PDF] Characterization Of Hermitian Symmetric Spaces By Fundamental Forms eBook

Author : Jürgen Berndt
Publisher : Walter de Gruyter GmbH & Co KG
Page : 249 pages
File Size : 19,15 MB
Release : 2022-03-21
Category : Mathematics
ISBN : 311068991X

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Hermitian symmetric spaces are an important class of manifolds that can be studied with methods from Kähler geometry and Lie theory. This work gives an introduction to Hermitian symmetric spaces and their submanifolds, and presents classifi cation results for real hypersurfaces in these spaces, focusing on results obtained by Jürgen Berndt and Young Jin Suh in the last 20 years.

Author : Armand Borel
Publisher : Springer Science & Business Media
Page : 477 pages
File Size : 47,82 MB
Release : 2006-07-25
Category : Mathematics
ISBN : 0817644660

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Introduces uniform constructions of most of the known compactifications of symmetric and locally symmetric spaces, with emphasis on their geometric and topological structures Relatively self-contained reference aimed at graduate students and research mathematicians interested in the applications of Lie theory and representation theory to analysis, number theory, algebraic geometry and algebraic topology

Author : Joseph Albert Wolf
Publisher : American Mathematical Soc.
Page : 408 pages
File Size : 40,68 MB
Release : 2007
Category : Mathematics
ISBN : 0821842897

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This study starts with the basic theory of topological groups, harmonic analysis, and unitary representations. It then concentrates on geometric structure, harmonic analysis, and unitary representation theory in commutative spaces.

Author : Jacques Faraut
Publisher : Springer Science & Business Media
Page : 539 pages
File Size : 35,39 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461213665

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A number of important topics in complex analysis and geometry are covered in this excellent introductory text. Written by experts in the subject, each chapter unfolds from the basics to the more complex. The exposition is rapid-paced and efficient, without compromising proofs and examples that enable the reader to grasp the essentials. The most basic type of domain examined is the bounded symmetric domain, originally described and classified by Cartan and Harish- Chandra. Two of the five parts of the text deal with these domains: one introduces the subject through the theory of semisimple Lie algebras (Koranyi), and the other through Jordan algebras and triple systems (Roos). Larger classes of domains and spaces are furnished by the pseudo-Hermitian symmetric spaces and related R-spaces. These classes are covered via a study of their geometry and a presentation and classification of their Lie algebraic theory (Kaneyuki). In the fourth part of the book, the heat kernels of the symmetric spaces belonging to the classical Lie groups are determined (Lu). Explicit computations are made for each case, giving precise results and complementing the more abstract and general methods presented. Also explored are recent developments in the field, in particular, the study of complex semigroups which generalize complex tube domains and function spaces on them (Faraut). This volume will be useful as a graduate text for students of Lie group theory with connections to complex analysis, or as a self-study resource for newcomers to the field. Readers will reach the frontiers of the subject in a considerably shorter time than with existing texts.