Global differential geometry : the mathematical legacy of Alfred Gray : International Congress on Differential Geometry, September 18-23, 2000, Bilbao, Spain
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書誌事項
Global differential geometry : the mathematical legacy of Alfred Gray : International Congress on Differential Geometry, September 18-23, 2000, Bilbao, Spain
（Contemporary mathematics, v. 288）
American Mathematical Society, c2001
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Includes bibliographies
内容説明・目次
内容説明
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.
目次
On the formality problem for symplectic manifolds by I. K. Babenko and I. A. Taimanov Osculating tubes and self-linking for curves on the three-sphere by T. F. Banchoff Isoparametric functions and harmonic and minimal unit vector fields by E. Boeckx and L. Vanhecke The Seiberg-Witten equations and almost-Hermitian geometry by S. K. Donaldson Sculpture inspired by work with Alfred Gray: Kepler elliptic curves and minimal surface sculptures of the planets by H. Ferguson Mesoscopic curvature and hyperbolicity by M. Gromov Stable forms and special metrics by N. Hitchin A CR-momentum Ansatz for nilpotent groups by A. Huckleberry and M. Voller Can tangent sphere bundles over Riemannian manifolds have strictly positive sectional curvature? by O. Kowalski, M. Sekizawa, and Z. Vlasek Volumes of geodesic balls and spheres associated to a metric connection with torsion by V. Miquel Special isothermic surfaces and solitons by E. Musso and L. Nicolodi The isoperimetric and Willmore problems by A. Ros Almost parallel structures by S. Salamon Technical computing with Mathematica by P. Wellin Complex geometry and representations of Lie groups by J. A. Wolf On the volume of compact spacelike hypersurfaces with hyperbolic boundary in Minkowski space by J. A. Aledo and J. A. Pastor Stability of zero mean curvature surfaces in flat Lorentzian 4-manifolds by L. J. Alias and B. Palmer Hitchin-Kobayashi correspondence for equivariant bundles on $X\times \mathbb{P}^1$ by L. Alvarez-Consul and O. Garcia-Prada Hopf vesicles in $\textbf{S}^3(\mathbf{1})$ by J. Arroyo and O. J. Garay Invariant nearly Kahler $f$-structures on homogeneous spaces by V. V. Balashchenko An extension of A. Gray's investigations on small geodesic balls by N. Bokan, M. Djoric, and U. Simon An energy minimizing family of unit vector fields on odd-dimensional spheres by V. Borrelli, F. Brito, and O. Gil-Medrano Is it admissible to linearize the Einstein equation in the presence of matter? by L. Bruna and J. Girbau Solutions of some conformally invariant equations of the first order by J. Bures On biharmonic maps by R. Caddeo, S. Montaldo, and P. Piu Characterizations of Pfaffian systems. Consequences in dimension five by M. A. Canadas-Pinedo and C. Ruiz On a new class of contact Riemannian manifolds by J. T. Cho Description of (1, 2)-symplectic metrics on flag manifolds by N. Cohen, C. J. C. Negreiros, and L. A. B. San Martin Complex surfaces with Betti numbers $b_1=1$, $b_2>0$ and finite quotients by G. Dloussky Hypercomplex nilpotent Lie groups by I. G. Dotti and A. Fino $\mathfrak{C}$-spaces of Iwasawa type and Damek-Ricci spaces by M. J. Druetta Deformations of constant mean curvature surfaces in half space models by M. E. E. L. Galvao and C. C. Goes The geometry of the skew-symmetric curvature operator in the complex setting by P. Gilkey and R. Ivanova Representing minimal curves in $\mathbb{C}^3$ by differential operators by H. Gollek Isometric immersions without positive Ricci curvature by L. Guijarro Natural Poisson and Jacobi structures on the tangent bundle of a pseudo-Riemannian manifold by J. Janyska On Alfred Gray's elliptical catenoid by H. Jimenez and S. Lopez de Medrano Sub-Riemannian geometry and non-holonomic mechanics by J. Koiller, P. R. Rodrigues, and P. Pitanga Weil algebras of generalized higher order velocities bundles by M. Kures The variety of Lie algebras from certain Riemannian viewpoint by J. Lauret How to use $\text{Mathematica}^{TM}$ to find cyclic surfaces of constant curvature in Lorentz-Minkowski space by R. Lopez The Fuglede-Ishihara and Baird-Eells theorems for $p>1$ by E. Loubeau Cohomology of nilmanifolds and Gontcharova's theorem by D. V. Millionschikov Asymptotically holomorphic embeddings of contact manifolds in projective spaces by V. Munoz, F. Presas, and I. Sols Convergent star products on Fr{e}chet linear Poisson algebras of Heisenberg type by H. Omori, Y. Maeda, N. Miyazaki, and A. Yoshioka Resolutions of 2-polyhedra by fake surfaces and embedings into $\mathbb{R}^4$ by A. Onischenko, D. Repovs, and A. Skopenkov Cayley 4-frames and a quaternion Kahler reduction related to ${\mathrm{Spin}(7)}$ by L. Ornea and P. Piccinni Old and new structures on products of spheres by M. Parton 1-Homogeneous sprays in Finsler manifolds by L. Del Riego The Gysin sequence for riemannian flows by J. I. R. Prieto On contact groupoids and Legendre bisections by T. Rybicki Affine maximal tori intersecting a fixed one by M. Salvai On the asymptotic series of the heat content by A. Savo Visualization of flat slant surfaces in ${\mathbb C}^2$ by Y. Tazawa On solvable Lie groups without lattices by A. Tralle Where does geometry go? A research and education perspective by J.-P. Bourguignon, E. Calabi, J. Eells, O. Garcia-Prada, and M. Gromov.
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