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Saturday, July 25, 2020 | History

8 edition of Differential geometry, Lie groups, and symmetric spaces over general base fields and rings found in the catalog.

Differential geometry, Lie groups, and symmetric spaces over general base fields and rings

by Wolfgang Bertram

  • 114 Want to read
  • 20 Currently reading

Published by American Mathematical Society in Providence, R.I .
Written in English

    Subjects:
  • Infinite dimensional Lie algebras,
  • Infinite-dimensional manifolds,
  • Symmetric spaces,
  • Geometry, Differential

  • Edition Notes

    Includes bibliographical references (p. 199-202).

    StatementWolfgang Bertram.
    SeriesMemoirs of the American Mathematical Society -- no. 900
    Classifications
    LC ClassificationsQA252.3 .B47 2008
    The Physical Object
    Paginationix, 202 p. :
    Number of Pages202
    ID Numbers
    Open LibraryOL16718133M
    ISBN 100821840916
    ISBN 109780821840917
    LC Control Number2007060585

      For Lie groups, a significant amount of analysis either begins with or reduces to analysis on homogeneous spaces, frequently on symmetric spaces. For many years and for many mathematicians, Sigurdur Helgason's classic Differential Geometry, Lie Groups, and Symmetric Spaces has been-and continues to be-the standard source for this s: 4. Differential Geometry, Lie Groups, and Symmetric Spaces Sigurdur Helgason Graduate Studies in Mathematics Elementary Differential Geometry 1. Manifolds 2 2. Tensor Fields 8 1. Vector Fields and 1-Forms 8 2. Tensor Algebra 13 The Simple Lie Algebras over C .

    Differential geometry was originally the geometry of curves and surfaces; the analytic study of geometric objects. We'll be dealing with manifolds ; a manifold could be described either as the abstraction of the notion of a smooth surface, or as the most general structure in which it makes sense to discuss the concept of a differentiable function. For Lie groups, a significant amount of analysis either begins with or reduces to analysis on homogeneous spaces, frequently on symmetric spaces. For many years and for many mathematicians, Sigurdur Helgason's classic Differential Geometry, Lie Groups, and Symmetric Spaces has been--and continues to be--the standard source for this material.

      Lie Groups, Physics, and Geometry Prof. Robert Gilmore Physics Department Email: [email protected] This book has been published by Cambridge University Press during Janaury, (ISBN13 ). Previous reviewers have praised this book for its precision and logical coherence, and these are accurate assessments, but not the whole story. When using this book for a course in Lie Groups, taught by Professor Helgason himself, I found this book severely lacking. Take for example Chapter I, which covers some basic differential s: 4.


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Differential geometry, Lie groups, and symmetric spaces over general base fields and rings by Wolfgang Bertram Download PDF EPUB FB2

Previous reviewers have praised this book for its precision and logical coherence, and these are accurate assessments, but not the whole story. When using this book for a course in Lie Groups, taught by Professor Helgason himself, I found this book severely lacking.

Take for example Chapter I, which covers some basic differential geometry/5(6). Differential Geometry, Lie Groups and Symmetric Spaces over General Base Fields and Rings. The aim of this work is to lay the foundations of differential geometry and Lie theory over the general class of topological base fields and -rings for which a differential calculus has been developed in recent work (collaboration with H.

Gloeckner and K.-H. Neeb), without any restriction on the. The sequels to the present book are published in the AMS's Mathematical Surveys and Monographs Series: Groups and Geometric Analysis, Vol and Geometric Analysis on Symmetric Spaces, Volume Sigurdur Helgason was awarded the Steele Prize for Differential Geometry, Lie Groups, and Symmetric Spaces and Groups and Geometric by:   Differential geometry aim of this work is to lay the foundations of differential geometry and Lie theory over the general class of topological base fields and -rings for which a differential calculus has been developed in recent work (collaboration with H.

Gloeckner and K.-H. Nee), without any restriction on the dimension or on the by: 2. Abstract: The aim of this work is to lay the foundations of differential geometry and Lie theory over the general class of topological base fields and -rings for which a differential calculus has been developed in recent work (collaboration with H.

Gloeckner and K.-H. Neeb), without any restriction on the dimension or on the characteristic. Two basic features distinguish our Lie groups from the Cited by: 2. Abstract: The aim of this work is to lay the foundations of differential geometry and Lie theory over the general class of topological base fields and -rings for which a differential calculus has been developed in recent work (collaboration with H.

Gloeckner and K.-H. Neeb), without any restriction on the dimension or on the characteristic. Two basic features distinguish our approach from the. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Abstract.

The aim of this work is to lay the foundations of differential geometry and Lie theory over the general class of topological base fields and-rings for which a differential calculus has been developed in [BGN04], without any restriction on the dimension or on the characteristic.

Differential Geometry And Symmetric Spaces by, Differential Geometry, Lie Groups and Symmetric Spaces over General Base Fields and Rings. Authors: Wolfgang Bertram.

Categories: Mathematics. Type: BOOK - Published: - Publisher: American Mathematical Soc. Differential Geometry, Lie Groups and Symmetric Spaces over General Base Fields and Rings Wolfgang Bertram To cite this version: Wolfgang Bertram. Differential Geometry, Lie Groups and Symmetric Spaces over General Base Fields and Rings.

Memoirs of the American Mathematical Society, American Mathematical Society,00 (00), pp ￿hal. Additional topics include the role of harmonic theory, geometric vector fields on Riemannian manifolds, Lie groups, symmetric spaces, and symplectic and Hermitian vector bundles.

A consideration of other differential geometric structures concludes the text, including surveys of characteristic classes of principal bundles, Cartan connections Reviews: 9. The aim of this work is to lay the foundations of differential geometry and Lie theory over the general class of topological base fields and -rings for which a differential calculus has been developed, without any restriction on the dimension or on the characteristic.

CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): The aim of this work is to lay the foundations of differential geometry and Lie theory over the general class of topological base fields and-rings for which a differential calculus has been developed in [BGN04], without any restriction on the dimension or on the characteristic.

Differential geometry, Lie groups and symmetric spaces over general base fields and rings About this Title. Wolfgang Bertram. Publication: Memoirs of the American Mathematical Society. A brilliant book: rigorous, tightly organized, and covering a vast amount ofgood mathematics.

-- Barrett O'Neill, University of California. Renders a great service in permitting the non-specialist, with a minimumknowledge of differential geometry and Lie groups, an initiation to the theoryof symmetrical spaces. Differential Geometry, Lie Groups and Symmetric Spaces over General Base Fields and Rings Article in Memoirs of the American Mathematical Society () March with 39 ReadsAuthor: Wolfgang Bertram.

Get this from a library. Differential geometry, Lie groups and symmetric spaces over general base fields and rings. [Wolfgang Bertram]. Differential Geometry over General Base Fields and Rings Version to appear in the Memoirs of the AMS.

we will develop the theory over certain base rings so that, in general, there is no dimension at all. Thus, instead of opposing from which I first learned the theory of differential geometry, Lie groups and symmetric spaces.

Later I. Get this from a library. Differential geometry, Lie groups, and symmetric spaces over general base fields and rings. [Wolfgang Bertram]. For Lie groups, a significant amount of analysis either begins with or reduces to analysis on homogeneous spaces, frequently on symmetric spaces.

For many years and for many mathematicians, Sigurdur Helgason's classic Differential Geometry, Lie Groups, and Symmetric Spaces has been--and continues to be--the standard source for this material. This book is one of _the_ classics in differential geometry.

It is the first and to date only book presenting the complete structure theory and classification of Riemannian symmetric spaces, together with the complete fundamentals in differential geometry and Lie groups needed to develop it.4/5(1). Abstract. The aim of this work is to lay the foundations of differential geometry and Lie theory over the general class of topological base fields and-rings for which a differential calculus has been developed in [BGN04], without any restriction on the dimension or on the : Wolfgang Bertram.The present book is intended as a textbook and reference work on three topics in the title.

Together with a volume in progress on "Groups and Geometric Analysis" it supersedes my "Differential Geometry and Symmetric Spaces," published in Differential geometry, Lie groups, and symmetric spaces over general base fields and rings / Material Type: Document, Internet resource: Document Type: Internet Resource, Computer File: All Authors / Contributors: Wolfgang Bertram.