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Softcover ISBN:  9780821827505 
Product Code:  CONM/288 
List Price:  $130.00 
MAA Member Price:  $117.00 
AMS Member Price:  $104.00 
eBook ISBN:  9780821878781 
Product Code:  CONM/288.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9780821827505 
eBook ISBN:  9780821878781 
Product Code:  CONM/288.B 
List Price:  $255.00 $192.50 
MAA Member Price:  $229.50 $173.25 
AMS Member Price:  $204.00 $154.00 

Book DetailsContemporary MathematicsVolume: 288; 2001; 457 ppMSC: Primary 22; 53
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.
ReadershipGraduate students and researchers interested in differential geometry, algebraic geometry and physics; scientists in related areas.

Table of Contents

Articles

Ivan K. Babenko and Iskander A. Taimanov — On the formality problem for symplectic manifolds [ MR 1870995 ]

Thomas F. Banchoff — Osculating tubes and selflinking for curves on the threesphere [ MR 1870996 ]

E. Boeckx and L. Vanhecke — Isoparametric functions and harmonic and minimal unit vector fields [ MR 1870997 ]

S. K. Donaldson — The SeibergWitten equations and almostHermitian geometry [ MR 1870998 ]

Helaman Ferguson — Sculpture inspired by work with Alfred Gray: Kepler elliptic curves and minimal surface sculptures of the planets [ MR 1870999 ]

Misha Gromov — Mesoscopic curvature and hyperbolicity [ MR 1871000 ]

Nigel Hitchin — Stable forms and special metrics [ MR 1871001 ]

A. Huckleberry and M. Völler — A CRmomentum ansatz for nilpotent groups [ MR 1871002 ]

O. Kowalski, M. Sekizawa and Z. Vlášek — Can tangent sphere bundles over Riemannian manifolds have strictly positive sectional curvature? [ MR 1871003 ]

Vicente Miquel — Volumes of geodesic balls and spheres associated to a metric connection with torsion [ MR 1871004 ]

Emilio Musso and Lorenzo Nicolodi — Special isothermic surfaces and solitons [ MR 1871005 ]

Antonio Ros — The isoperimetric and Willmore problems [ MR 1871006 ]

Simon Salamon — Almost parallel structures [ MR 1871007 ]

Paul Wellin — Technical computing with Mathematica [ MR 1871008 ]

Joseph A. Wolf — Complex geometry and representations of Lie groups [ MR 1871009 ]

Juan A. Aledo and José A. Pastor — On the volume of compact spacelike hypersurfaces with hyperbolic boundary in Minkowski space [ MR 1871010 ]

Luis J. Alías and Bennett Palmer — Stability of zero mean curvature surfaces in flat Lorentzian $4$manifolds [ MR 1871011 ]

Luis ÁlvarezCónsul and Oscar GarcíaPrada — HitchinKobayashi correspondence for equivariant bundles on $X\times \Bbb P^1$ [ MR 1871012 ]

J. Arroyo and O. J. Garay — Hopf vesicles in $S^3(1)$ [ MR 1871013 ]

Vitaly V. Balashchenko — Invariant nearly Kähler $f$structures on homogeneous spaces [ MR 1871014 ]

N. Bokan, M. Djorić and U. Simon — An extension of A. Gray’s investigations on small geodesic balls [ MR 1871015 ]

Vincent Borrelli, Fabiano Brito and Olga GilMedrano — An energy minimizing family of unit vector fields on odddimensional spheres [ MR 1871016 ]

Lluís Bruna and Joan Girbau — Is it admissible to linearize the Einstein equation in the presence of matter? [ MR 1871017 ]

Jarolím Bureš — Solutions of some conformally invariant equations of the first order [ MR 1871018 ]

Renzo Caddeo, Stefano Montaldo and Paola Piu — On biharmonic maps [ MR 1871019 ]

María A. CañadasPinedo and Ceferino Ruiz — Characterizations of Pfaffian systems. Consequences in dimension five [ MR 1871020 ]

Jong Taek Cho — On a new class of contact Riemannian manifolds [ MR 1871021 ]

Nir Cohen, Caio J. C. Negreiros and Luiz A. B. San Martin — Description of $(1,2)$symplectic metrics on flag manifolds [ MR 1871022 ]

Georges Dloussky — Complex surfaces with Betti numbers $b_1=1,\ b_2>0$ and finite quotients [ MR 1871023 ]

Isabel G. Dotti and Anna Fino — Hypercomplex nilpotent Lie groups [ MR 1871024 ]

Maria J. Druetta — $\mathfrak {C}$spaces of Iwasawa type and DamekRicci spaces [ MR 1871025 ]

M. Elisa E. L. Galvão and Célia C. Góes — Deformations of constant mean curvature surfaces in half space models [ MR 1871026 ]

Peter Gilkey and Raina Ivanova — The geometry of the skewsymmetric curvature operator in the complex setting [ MR 1871027 ]

Hubert Gollek — Representing minimal curves in $\Bbb C^3$ by differential operators [ MR 1871028 ]

Luis Guijarro — Isometric immersions without positive Ricci curvature [ MR 1871029 ]

Josef Janyška — Natural Poisson and Jacobi structures on the tangent bundle of a pseudoRiemannian manifold [ MR 1871030 ]

Hugo Jiménez and Santiago López de Medrano — On Alfred Gray’s elliptical catenoid [ MR 1871031 ]

Jair Koiller, Paulo R. Rodrigues and Paulo Pitanga — SubRiemannian geometry and nonholonomic mechanics [ MR 1871032 ]

Miroslav Kureš — Weil algebras of generalized higher order velocities bundles [ MR 1871033 ]

Jorge Lauret — The variety of Lie algebras from certain Riemannian viewpoint [ MR 1871034 ]

Rafael López — How to use MATHEMATICA$^{\rm TM}$ to find cyclic surfaces of constant curvature in LorentzMinkowski space [ MR 1871035 ]

E. Loubeau — The FugledeIshihara and BairdEells theorems for $p>1$ [ MR 1871036 ]

Dmitri V. Millionschikov — Cohomology of nilmanifolds and Gontcharova’s theorem [ MR 1871037 ]

Vicente Muñoz, Fran Presas and Ignacio Sols — Asymptotically holomorphic embeddings of contact manifolds in projective spaces [ MR 1871038 ]

Hideki Omori, Yoshiaki Maeda, Naoya Miyazaki and Akira Yoshioka — Convergent star products on Fréchet linear Poisson algebras of Heisenberg type [ MR 1871039 ]

Alexander Onischenko, Dušan Repovš and Arkady Skopenkov — Resolutions of $2$polyhedra by fake surfaces and embeddings into $\Bbb R^4$ [ MR 1871040 ]

Liviu Ornea and Paolo Piccinni — Cayley $4$frames and a quaternion Kähler reduction related to ${\rm Spin}(7)$ [ MR 1871042 ]

Maurizio Parton — Old and new structures on products of spheres [ MR 1871043 ]

L. Del Riego — $1$homogeneous sprays in Finsler manifolds [ MR 1871044 ]

José Ignacio Royo Prieto — The Gysin sequence for Riemannian flows [ MR 1871045 ]

Tomasz Rybicki — On contact groupoids and Legendre bisections [ MR 1871046 ]

Marcos Salvai — Affine maximal tori intersecting a fixed one [ MR 1871047 ]

Alessandro Savo — On the asymptotic series of the heat content [ MR 1871048 ]

Yoshihiko Tazawa — Visualization of flat slant surfaces in $\Bbb C^2$ [ MR 1871049 ]

Aleksy Tralle — On solvable Lie groups without lattices [ MR 1871050 ]

JeanPierre Bourguignon, Eugenio Calabi, James Eells, Oscar GarciaPrada and Misha Gromov — Where does geometry go? A research and education perspective [ MR 1871051 ]


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

Articles

Ivan K. Babenko and Iskander A. Taimanov — On the formality problem for symplectic manifolds [ MR 1870995 ]

Thomas F. Banchoff — Osculating tubes and selflinking for curves on the threesphere [ MR 1870996 ]

E. Boeckx and L. Vanhecke — Isoparametric functions and harmonic and minimal unit vector fields [ MR 1870997 ]

S. K. Donaldson — The SeibergWitten equations and almostHermitian geometry [ MR 1870998 ]

Helaman Ferguson — Sculpture inspired by work with Alfred Gray: Kepler elliptic curves and minimal surface sculptures of the planets [ MR 1870999 ]

Misha Gromov — Mesoscopic curvature and hyperbolicity [ MR 1871000 ]

Nigel Hitchin — Stable forms and special metrics [ MR 1871001 ]

A. Huckleberry and M. Völler — A CRmomentum ansatz for nilpotent groups [ MR 1871002 ]

O. Kowalski, M. Sekizawa and Z. Vlášek — Can tangent sphere bundles over Riemannian manifolds have strictly positive sectional curvature? [ MR 1871003 ]

Vicente Miquel — Volumes of geodesic balls and spheres associated to a metric connection with torsion [ MR 1871004 ]

Emilio Musso and Lorenzo Nicolodi — Special isothermic surfaces and solitons [ MR 1871005 ]

Antonio Ros — The isoperimetric and Willmore problems [ MR 1871006 ]

Simon Salamon — Almost parallel structures [ MR 1871007 ]

Paul Wellin — Technical computing with Mathematica [ MR 1871008 ]

Joseph A. Wolf — Complex geometry and representations of Lie groups [ MR 1871009 ]

Juan A. Aledo and José A. Pastor — On the volume of compact spacelike hypersurfaces with hyperbolic boundary in Minkowski space [ MR 1871010 ]

Luis J. Alías and Bennett Palmer — Stability of zero mean curvature surfaces in flat Lorentzian $4$manifolds [ MR 1871011 ]

Luis ÁlvarezCónsul and Oscar GarcíaPrada — HitchinKobayashi correspondence for equivariant bundles on $X\times \Bbb P^1$ [ MR 1871012 ]

J. Arroyo and O. J. Garay — Hopf vesicles in $S^3(1)$ [ MR 1871013 ]

Vitaly V. Balashchenko — Invariant nearly Kähler $f$structures on homogeneous spaces [ MR 1871014 ]

N. Bokan, M. Djorić and U. Simon — An extension of A. Gray’s investigations on small geodesic balls [ MR 1871015 ]

Vincent Borrelli, Fabiano Brito and Olga GilMedrano — An energy minimizing family of unit vector fields on odddimensional spheres [ MR 1871016 ]

Lluís Bruna and Joan Girbau — Is it admissible to linearize the Einstein equation in the presence of matter? [ MR 1871017 ]

Jarolím Bureš — Solutions of some conformally invariant equations of the first order [ MR 1871018 ]

Renzo Caddeo, Stefano Montaldo and Paola Piu — On biharmonic maps [ MR 1871019 ]

María A. CañadasPinedo and Ceferino Ruiz — Characterizations of Pfaffian systems. Consequences in dimension five [ MR 1871020 ]

Jong Taek Cho — On a new class of contact Riemannian manifolds [ MR 1871021 ]

Nir Cohen, Caio J. C. Negreiros and Luiz A. B. San Martin — Description of $(1,2)$symplectic metrics on flag manifolds [ MR 1871022 ]

Georges Dloussky — Complex surfaces with Betti numbers $b_1=1,\ b_2>0$ and finite quotients [ MR 1871023 ]

Isabel G. Dotti and Anna Fino — Hypercomplex nilpotent Lie groups [ MR 1871024 ]

Maria J. Druetta — $\mathfrak {C}$spaces of Iwasawa type and DamekRicci spaces [ MR 1871025 ]

M. Elisa E. L. Galvão and Célia C. Góes — Deformations of constant mean curvature surfaces in half space models [ MR 1871026 ]

Peter Gilkey and Raina Ivanova — The geometry of the skewsymmetric curvature operator in the complex setting [ MR 1871027 ]

Hubert Gollek — Representing minimal curves in $\Bbb C^3$ by differential operators [ MR 1871028 ]

Luis Guijarro — Isometric immersions without positive Ricci curvature [ MR 1871029 ]

Josef Janyška — Natural Poisson and Jacobi structures on the tangent bundle of a pseudoRiemannian manifold [ MR 1871030 ]

Hugo Jiménez and Santiago López de Medrano — On Alfred Gray’s elliptical catenoid [ MR 1871031 ]

Jair Koiller, Paulo R. Rodrigues and Paulo Pitanga — SubRiemannian geometry and nonholonomic mechanics [ MR 1871032 ]

Miroslav Kureš — Weil algebras of generalized higher order velocities bundles [ MR 1871033 ]

Jorge Lauret — The variety of Lie algebras from certain Riemannian viewpoint [ MR 1871034 ]

Rafael López — How to use MATHEMATICA$^{\rm TM}$ to find cyclic surfaces of constant curvature in LorentzMinkowski space [ MR 1871035 ]

E. Loubeau — The FugledeIshihara and BairdEells theorems for $p>1$ [ MR 1871036 ]

Dmitri V. Millionschikov — Cohomology of nilmanifolds and Gontcharova’s theorem [ MR 1871037 ]

Vicente Muñoz, Fran Presas and Ignacio Sols — Asymptotically holomorphic embeddings of contact manifolds in projective spaces [ MR 1871038 ]

Hideki Omori, Yoshiaki Maeda, Naoya Miyazaki and Akira Yoshioka — Convergent star products on Fréchet linear Poisson algebras of Heisenberg type [ MR 1871039 ]

Alexander Onischenko, Dušan Repovš and Arkady Skopenkov — Resolutions of $2$polyhedra by fake surfaces and embeddings into $\Bbb R^4$ [ MR 1871040 ]

Liviu Ornea and Paolo Piccinni — Cayley $4$frames and a quaternion Kähler reduction related to ${\rm Spin}(7)$ [ MR 1871042 ]

Maurizio Parton — Old and new structures on products of spheres [ MR 1871043 ]

L. Del Riego — $1$homogeneous sprays in Finsler manifolds [ MR 1871044 ]

José Ignacio Royo Prieto — The Gysin sequence for Riemannian flows [ MR 1871045 ]

Tomasz Rybicki — On contact groupoids and Legendre bisections [ MR 1871046 ]

Marcos Salvai — Affine maximal tori intersecting a fixed one [ MR 1871047 ]

Alessandro Savo — On the asymptotic series of the heat content [ MR 1871048 ]

Yoshihiko Tazawa — Visualization of flat slant surfaces in $\Bbb C^2$ [ MR 1871049 ]

Aleksy Tralle — On solvable Lie groups without lattices [ MR 1871050 ]

JeanPierre Bourguignon, Eugenio Calabi, James Eells, Oscar GarciaPrada and Misha Gromov — Where does geometry go? A research and education perspective [ MR 1871051 ]