Contemporary Mathematics 2001; 457 pp; softcover Volume: 288 ISBN10: 0821827502 ISBN13: 9780821827505 List Price: US$137 Member Price: US$109.60 Order Code: CONM/288
 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. Readership Graduate students and researchers interested in differential geometry, algebraic geometry and physics; scientists in related areas. Table of Contents  I. K. Babenko and I. A. Taimanov  On the formality problem for symplectic manifolds
 T. F. Banchoff  Osculating tubes and selflinking for curves on the threesphere
 E. Boeckx and L. Vanhecke  Isoparametric functions and harmonic and minimal unit vector fields
 S. K. Donaldson  The SeibergWitten equations and almostHermitian geometry
 H. Ferguson  Sculpture inspired by work with Alfred Gray: Kepler elliptic curves and minimal surface sculptures of the planets
 M. Gromov  Mesoscopic curvature and hyperbolicity
 N. Hitchin  Stable forms and special metrics
 A. Huckleberry and M. Völler  A CRmomentum Ansatz for nilpotent groups
 O. Kowalski, M. Sekizawa, and Z. Vlášek  Can tangent sphere bundles over Riemannian manifolds have strictly positive sectional curvature?
 V. Miquel  Volumes of geodesic balls and spheres associated to a metric connection with torsion
 E. Musso and L. Nicolodi  Special isothermic surfaces and solitons
 A. Ros  The isoperimetric and Willmore problems
 S. Salamon  Almost parallel structures
 P. Wellin  Technical computing with Mathematica
 J. A. Wolf  Complex geometry and representations of Lie groups
 J. A. Aledo and J. A. Pastor  On the volume of compact spacelike hypersurfaces with hyperbolic boundary in Minkowski space
 L. J. Alías and B. Palmer  Stability of zero mean curvature surfaces in flat Lorentzian 4manifolds
 L. ÁlvarezCónsul and O. GarcíaPrada  HitchinKobayashi correspondence for equivariant bundles on \(X\times \mathbb{P}^1\)
 J. Arroyo and O. J. Garay  Hopf vesicles in \(\mathbf{S}^3(\mathbf{1})\)
 V. V. Balashchenko  Invariant nearly Kähler \(f\)structures on homogeneous spaces
 N. Bokan, M. Djorić, and U. Simon  An extension of A. Gray's investigations on small geodesic balls
 V. Borrelli, F. Brito, and O. GilMedrano  An energy minimizing family of unit vector fields on odddimensional spheres
 L. Bruna and J. Girbau  Is it admissible to linearize the Einstein equation in the presence of matter?
 J. Bureš  Solutions of some conformally invariant equations of the first order
 R. Caddeo, S. Montaldo, and P. Piu  On biharmonic maps
 M. A. CañadasPinedo and C. Ruiz  Characterizations of Pfaffian systems. Consequences in dimension five
 J. T. Cho  On a new class of contact Riemannian manifolds
 N. Cohen, C. J. C. Negreiros, and L. A. B. San Martin  Description of (1, 2)symplectic metrics on flag manifolds
 G. Dloussky  Complex surfaces with Betti numbers \(b_1=1\), \(b_2>0\) and finite quotients
 I. G. Dotti and A. Fino  Hypercomplex nilpotent Lie groups
 M. J. Druetta  \(\mathfrak{C}\)spaces of Iwasawa type and DamekRicci spaces
 M. E. E. L. Galvão and C. C. Góes  Deformations of constant mean curvature surfaces in half space models
 P. Gilkey and R. Ivanova  The geometry of the skewsymmetric curvature operator in the complex setting
 H. Gollek  Representing minimal curves in \(\mathbb{C}^3\) by differential operators
 L. Guijarro  Isometric immersions without positive Ricci curvature
 J. Janyška  Natural Poisson and Jacobi structures on the tangent bundle of a pseudoRiemannian manifold
 H. Jiménez and S. López de Medrano  On Alfred Gray's elliptical catenoid
 J. Koiller, P. R. Rodrigues, and P. Pitanga  SubRiemannian geometry and nonholonomic mechanics
 M. Kureš  Weil algebras of generalized higher order velocities bundles
 J. Lauret  The variety of Lie algebras from certain Riemannian viewpoint
 R. López  How to use \(\text{Mathematica}^{\mathrm{TM}}\) to find cyclic surfaces of constant curvature in LorentzMinkowski space
 E. Loubeau  The FugledeIshihara and BairdEells theorems for \(p>1\)
 D. V. Millionschikov  Cohomology of nilmanifolds and Gontcharova's theorem
 V. Muñoz, F. Presas, and I. Sols  Asymptotically holomorphic embeddings of contact manifolds in projective spaces
 H. Omori, Y. Maeda, N. Miyazaki, and A. Yoshioka  Convergent star products on Fr{é}chet linear Poisson algebras of Heisenberg type
 A. Onischenko, D. Repovš, and A. Skopenkov  Resolutions of 2polyhedra by fake surfaces and embedings into \(\mathbb{R}^4\)
 L. Ornea and P. Piccinni  Cayley 4frames and a quaternion Kähler reduction related to \({\mathrm{Spin}(7)}\)
 M. Parton  Old and new structures on products of spheres
 L. Del Riego  1Homogeneous sprays in Finsler manifolds
 J. I. R. Prieto  The Gysin sequence for riemannian flows
 T. Rybicki  On contact groupoids and Legendre bisections
 M. Salvai  Affine maximal tori intersecting a fixed one
 A. Savo  On the asymptotic series of the heat content
 Y. Tazawa  Visualization of flat slant surfaces in \({\mathbb C}^2\)
 A. Tralle  On solvable Lie groups without lattices
 J.P. Bourguignon, E. Calabi, J. Eells, O. GarciaPrada, and M. Gromov  Where does geometry go? A research and education perspective
