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Global Differential Geometry: The Mathematical Legacy of Alfred Gray
Edited by: Marisa Fernández, University of the Basque Country, Bilbao, Spain, and Joseph A. Wolf, University of California at Berkeley, CA
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Contemporary Mathematics
2001; 457 pp; softcover
Volume: 288
ISBN-10: 0-8218-2750-2
ISBN-13: 978-0-8218-2750-5
List Price: US$137
Member Price: US$109.60
Order Code: CONM/288
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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 self-linking for curves on the three-sphere
  • E. Boeckx and L. Vanhecke -- Isoparametric functions and harmonic and minimal unit vector fields
  • S. K. Donaldson -- The Seiberg-Witten equations and almost-Hermitian 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 CR-momentum 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 4-manifolds
  • L. Álvarez-Cónsul and O. García-Prada -- Hitchin-Kobayashi 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. Gil-Medrano -- An energy minimizing family of unit vector fields on odd-dimensional 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. Cañadas-Pinedo 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 Damek-Ricci 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 skew-symmetric 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 pseudo-Riemannian manifold
  • H. Jiménez and S. López de Medrano -- On Alfred Gray's elliptical catenoid
  • J. Koiller, P. R. Rodrigues, and P. Pitanga -- Sub-Riemannian geometry and non-holonomic 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 Lorentz-Minkowski space
  • E. Loubeau -- The Fuglede-Ishihara and Baird-Eells 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 2-polyhedra by fake surfaces and embedings into \(\mathbb{R}^4\)
  • L. Ornea and P. Piccinni -- Cayley 4-frames and a quaternion Kähler reduction related to \({\mathrm{Spin}(7)}\)
  • M. Parton -- Old and new structures on products of spheres
  • L. Del Riego -- 1-Homogeneous 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. Garcia-Prada, and M. Gromov -- Where does geometry go? A research and education perspective
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