Topics in Geometry

1. Front Matter

   Pages i-xxi

   PDF

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

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.

• Congruence
• Lie
• Mathematica
• Natural
• Scala
• Volume
• boundary element method
• curvature
• equation
• geometry
• lie group
• memory
• theorem
• time
• vertices

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

  Simon Gindikin

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