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Topics in Geometry

In Memory of Joseph D’Atri

  • Book
  • © 1996

Overview

Editors:
  1. Simon Gindikin

    1. Department of Mathematics, Rutgers University, New Brunswick, USA

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Part of the book series: Progress in Nonlinear Differential Equations and Their Applications (PNLDE, volume 20)

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-xxi
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  2. Non-Linear Elliptic Equations on Riemannian Manifolds with the Sobolev Critical Exponent

    • A. Bahri, H. Brezis
    Pages 1-100

  3. Symmetric Cones

    • Josef Dorfmeister
    Pages 101-121

  4. Pseudo-Hermitian Symmetric Spaces of Tube Type

    • Jacques Faraut, Simon Gindikin
    Pages 123-154

  5. Homogeneous Riemannian Manifolds Whose Geodesies Are Orbits

    • Carolyn S. Gordon
    Pages 155-174

  6. On the D-Module and Formal-Variable Approaches to Vertex Algebras

    • Yi-Zhi Huang, James Lepowsky
    Pages 175-202

  7. The Lowest Eigenvalue for Congruence Groups

    • Henryk Iwaniec
    Pages 203-212

  8. Signatures of Roots and a New Characterization of Causal Symmetric Spaces

    • Soji Kaneyuki
    Pages 213-229

  9. Admissible Limit Sets of Discrete Groups On Symmetric Spaces of Rank One

    • Adam Korányi
    Pages 231-240

  10. D’Atri Spaces

    • Oldřich Kowalski, Friedbert Prüfer, Lieven Vanhecke
    Pages 241-284

  11. Multiple Point Blowup Phenomenon in Scalar Curvature Equations on Spheres of Dimension Greater Than Three

    • Yanyan Li
    Pages 285-294

  12. The Harish-Chandra Realization for Non-Symmetric Domains in ℂn

    • R. Penney
    Pages 295-314

  13. How Many Lorentz Surfaces Are There?

    • Robert Smyth, Tilla Weinstein
    Pages 315-330

  14. On a Theorem of Milnor and Thom

    • Nolan R. Wallach
    Pages 331-348

  15. Riemannian Exponential Maps and Decompositions of Reductive Lie Groups

    • Joseph A. Wolf, Roger Zierau
    Pages 349-354

  16. Weakly Symmetric Spaces

    • Wolfgang Ziller
    Pages 355-368
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Keywords

About this book

This collection of articles serves to commemorate the legacy of Joseph D'Atri, who passed away on April 29, 1993, a few days after his 55th birthday. Joe D' Atri is credited with several fundamental discoveries in ge­ ometry. In the beginning of his mathematical career, Joe was interested in the generalization of symmetrical spaces in the E. Cart an sense. Symmetric spaces, differentiated from other homogeneous manifolds by their geomet­ rical richness, allows the development of a deep analysis. Geometers have been constantly interested and challenged by the problem of extending the class of symmetric spaces so as to preserve their geometrical and analytical abundance. The name of D'Atri is tied to one of the most successful gen­ eralizations: Riemann manifolds in which (local) geodesic symmetries are volume-preserving (up to sign). In time, it turned out that the majority of interesting generalizations of symmetrical spaces are D'Atri spaces: natu­ ral reductive homogeneous spaces, Riemann manifolds whose geodesics are orbits of one-parameter subgroups, etc. The central place in D'Atri's research is occupied by homogeneous bounded domains in en, which are not symmetric. Such domains were discovered by Piatetskii-Shapiro in 1959, and given Joe's strong interest in the generalization of symmetric spaces, it was very natural for him to direct his research along this path.

Editors and Affiliations

  • Department of Mathematics, Rutgers University, New Brunswick, USA

    Simon Gindikin

Bibliographic Information

  • Book Title: Topics in Geometry

  • Book Subtitle: In Memory of Joseph D’Atri

  • Editors: Simon Gindikin

  • Series Title: Progress in Nonlinear Differential Equations and Their Applications

  • DOI: https://doi.org/10.1007/978-1-4612-2432-7

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Boston 1996

  • Hardcover ISBN: 978-0-8176-3828-3Due: 27 June 1996

  • Softcover ISBN: 978-1-4612-7534-3Published: 30 September 2011

  • eBook ISBN: 978-1-4612-2432-7Published: 06 December 2012

  • Series ISSN: 1421-1750

  • Series E-ISSN: 2374-0280

  • Edition Number: 1

  • Number of Pages: XXII, 370

  • Topics: Geometry

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