**Contemporary Mathematics**

Volume: 288;
2001;
457 pp;
Softcover

MSC: Primary 22; 53;

Print ISBN: 978-0-8218-2750-5

Product Code: CONM/288

List Price: $137.00

Individual Member Price: $109.60

**Electronic ISBN: 978-0-8218-7878-1
Product Code: CONM/288.E**

List Price: $137.00

Individual Member Price: $109.60

# Global Differential Geometry: The Mathematical Legacy of Alfred Gray

Share this page *Edited by *
*Marisa Fernández; Joseph A. Wolf*

Alfred Gray's work covered a great part of differential geometry. In September 2000, a remarkable International Congress on Differential Geometry was held in his memory in Bilbao, Spain. Mathematicians from all over the world, representing 24 countries, attended the event.

This volume includes major contributions by well known mathematicians (T. Banchoff, S. Donaldson, H. Ferguson, M. Gromov, N. Hitchin, A. Huckleberry, O. Kowalski, V. Miquel, E. Musso, A. Ros, S. Salamon, L. Vanhecke, P. Wellin and J.A. Wolf), the interesting discussion from the round table moderated by J.-P. Bourguignon, and a carefully selected and refereed selection of the Short Communications presented at the Congress.

This book represents the state of the art in modern differential geometry, with some general expositions of some of the more active areas: special Riemannian manifolds, Lie groups and homogeneous spaces, complex structures, symplectic manifolds, geometry of geodesic spheres and tubes and related problems, geometry of surfaces, and computer graphics in differential geometry.

#### Table of Contents

# Table of Contents

## Global Differential Geometry: The Mathematical Legacy of Alfred Gray

- Contents vii8 free
- Foreword xi12 free
- Preface xiii14 free
- Photograph of Alfred Gray Memorial Bronze xiv15 free
- Acknowledgements xv16 free
- List of publications of Alfred Gray xvii18 free
- List of participants xxvii28 free
- Invited contributions 132 free
- On the formality problem for symplectic manifolds 132
- Osculating tubes and self-linking for curves on the three-sphere 1041
- Isoparametric functions and harmonic and minimal unit vector fields 2051
- The Seiberg-Witten equations and almost-Hermitian geometry 3263
- Sculpture inspired by work with Alfred Gray: Kepler elliptic curves and minimal surface sculptures of the planets 3970
- Mesoscopic curvature and hyperbolicity 5889
- Stable forms and special metrics 70101
- A CR-Momentum Ansatz for nilpotent groups 90121
- Can tangent sphere bundles over Riemannian manifolds have strictly positive sectional curvature? 110141
- Volumes of geodesic balls and spheres associated to a metric connection with torsion 119150
- The isoperimetric and Willmore problems 149180
- Almost parallel structures 162193
- Technical computing with Mathematica 182213
- Complex geometry and representations of Lie groups 202233

- Communications 239270
- On the volume of compact spacelike hypersurfaces with hyperbolic boundary in Minkowski space 239270
- Stability of zero mean curvature surfaces in flat Lorentzian 4-manifolds 244275
- Hitchin-Kobayashi correspondence for equivariant bundles on X x P1 249280
- Invariant nearly Kähler f-structures on homogeneous spaces 263294
- An extension of A. Gray's investigations on small geodesic balls 268299
- An energy minimizing family of unit vector fields on odd-dimensional spheres 273304
- Is it admissible to linearize the Einstein equation in the presence of matter? 277308
- Solutions of some conformally invariant equations of the first order 281312
- On biharmonic maps 286317
- Characterizations of Pfaffian systems. Consequences in dimension five 291322
- On a new class of contact Riemannian manifolds 296327
- Description of (1, 2)-symplectic metrics on flag manifolds 300331
- Complex surfaces with Betti numbers b1=1, b2 > 0 and finite quotients 305336
- Hypercomplex nilpotent Lie groups 310341
- C-spaces of Iwasawa type and Damek-Ricci spaces 315346
- Deformations of constant mean curvature surfaces in half space models 320351
- The geometry of the skew-symmetric curvature operator in the complex setting 325356
- Representing minimal curves in C3 by differential operators 334365
- Isometric immersions without positive Ricci curvature 339370
- Natural Poisson and Jacobi structures on the tangent bundle of a pseudo-Riemannian manifold 343374
- On Alfred Gray's elliptical catenoid 348379
- Sub-Riemannian geometry and non-holonomic mechanics 353384
- Weil algebras of generalized higher order velocities bundles 358389
- How to a use MATHEMATICA ™ to find cyclic surfaces of constant curvature in Lorentz-Minkowski space 371402
- The Fuglede-Ishihara and Baird-Eells theorems for p > 1 376407
- Cohomology of nilmanifolds and Gontcharova's theorem 381412
- Asymptotically holomorphic embeddings of contact manifolds in projective spaces 386417
- Convergent star products on Fréchet linear Poisson algebras of Heisenberg type 391422
- Resolutions of 2-polyhedra by fake surfaces and embeddings into R4 396427
- Cayley 4-frames and a quaternion Kähler reduction related to Spin(7) 401432
- Old and new structures on products of spheres 406437
- !-Homogeneous sprays in Finsler manifolds 411442
- The Gysin sequence for riemannian flows 415446
- On contact groupoids and Legendre bisections 420451
- Affine maximal tori intersecting a fixed one 425456
- Visualization of flat slant surfaces in C2 433464
- On solvable Lie groups without lattices 437468

- Round Table Discussion 442473

#### Readership

Graduate students and researchers interested in differential geometry, algebraic geometry and physics; scientists in related areas.