Eugenio Calabi,
Jean-Pierre Bourguignon,
Xiuxiong Chen,
Simon Donaldson
e.a.
Springer Berlin Heidelberg
e druk, 2021
9783662621332
Collected Works
Specificaties
Gebonden, blz.
|
Engels
Springer Berlin Heidelberg |
e druk, 2021
ISBN13: 9783662621332
Rubricering
Verwachte levertijd ongeveer 9 werkdagen
Samenvatting
While Eugenio Calabi is best known for his contributions to the theory of Calabi-Yau manifolds, this Steele-Prize-winning geometer’s fundamental contributions to mathematics have been far broader and more diverse than might be guessed from this one aspect of his work. His works have deep influence and lasting impact in global differential geometry, mathematical physics and beyond. By bringing together 47 of Calabi’s important articles in a single volume, this book provides a comprehensive overview of his mathematical oeuvre, and includes papers on complex manifolds, algebraic geometry, Kähler metrics, affine geometry, partial differential equations, several complex variables, group actions and topology. The volume also includes essays on Calabi’s mathematics by several of his mathematical admirers, including S.K. Donaldson, B. Lawson and S.-T. Yau, Marcel Berger; and Jean Pierre Bourguignon. This book is intended for mathematicians and graduate students around the world. Calabi’s visionary contributions will certainly continue to shape the course of this subject far into the future.
Specificaties
ISBN13:9783662621332
Taal:Engels
Bindwijze:gebonden
Uitgever:Springer Berlin Heidelberg
Inhoudsopgave
<p>Preface.- J.-P. Bourguignon, Eugenio Calabi’s Short Biography.- Bibliographic List of Works.- S.-T. Yau, An Essay on Eugenio Calabi.- Part I: Commentaries on Calabi’s Life and Work: B. Lawson, Reflections on the Early Work of Eugenio Calabi.- M. Berger, Encounter with a Geometer: Eugenio Calabi.- J.-P. Bourguignon, Eugenio Calabi and Kähler Metrics.- C. LeBrun, Eugenio Calabi and the Curvature of Kähler Manifolds.- X. Chen, S. Donaldson, Calabi’s Work on Affine Differential Geometry and Results of Bernstein Type.- Part II: Collected Works: E. Calabi ,Ar. Dvoretzky, Convergence- and Sum-Factors for Series of Complex Numbers (1951).- E. Calabi, D. C. Spencer, Completely Integrable Almost Complex Manifolds (1951).- E. Calabi, Metric Riemann Surfaces (1953).- E. Calabi, M. Rosenlicht, Complex Analytic Manifolds Without Countable Base (1953).- E. Calabi, B. Eckmann, A Class of Compact, Complex Manifolds Which Are Not Algebraic (1953).- E. Calabi, Isometric Imbedding of Complex Manifolds (1953).- E. Calabi, The Space of Kähler Metrics (1954).- E. Calabi, The Variation of Kähler Metrics I. The Structure of the Space (1954).- E. Calabi, The Variation of Kähler Metrics II. A Minimum Problem (1954).- E. Calabi, On Kähler Manifolds With Vanishing Canonical Class (1957).- E. Calabi, Construction and Properties of Some 6-Dimensional Almost Complex Manifolds (1958).- E. Calabi, Improper Affine Hyperspheres of Convex Type and a Generalization of a Theorem by K. Jörgens (1958).- E. Calabi, An Extension of E. Hopf’s Maximum Principle with an Application to Riemannian Geometry (1958).- E. Calabi, Errata: An Extension of E. Hopf’s Maximum Principle with an Application to Riemannian Geometry (1959).- E. Calabi, E. Vesentini, Sur les variétés complexes compactes localement symétriques (1959).- E. Calabi, E. Vesentini, On Compact, Locally Symmetric Kähler Manifolds (1960).- E. Calabi, On Compact, Riemannian Manifolds with Constant Curvature I. (1961).- E. Calabi, L. Markus Relativistic Space Forms (1962).- E. Calabi, Linear Systems of Real Quadratic Forms (1964).- E. Calabi, Quasi-Surjective Mappings and a Generalization of Morse Theory (1966).- E. Calabi, Minimal Immersions of Surfaces in Euclidean Spheres (1967).- E. Calabi, On Ricci Curvature and Geodesics (1967).- E. Calabi, On Differentiable Actions of Compact Lie Groups on Compact Manifolds (1968).- E. Calabi, An Intrinsic Characterization of Harmonic One-Forms (1969).- E. Calabi, On the Group of Automorphisms of a Symplectic Manifold (1970).- E. Calabi, P. Hartman, On the Smoothness of Isometries (1970).- E. Calabi, Examples of Bernstein Problems for Some Nonlinear Equations (1970).- E. Calabi, Über singuläre symplektische Strukturen (1971).- E. Calabi, Complete Affine Hyperspheres I (1972).- E. Calabi, A Construction of Nonhomogeneous Einstein Metrics (1975).- E. Calabi, H. S. Wilf, On the Sequential and Random Selection of Subspaces Over a Finite Field (1977).- E. Calabi, Métriques kählériennes et fibrés holomorphes (1978).- E. Calabi, Isometric Families of Kähler Structures (1980).- E. Calabi, Géométrie différentielle affine des hypersurfaces (1981).- E. Calabi, Linear Systems of Real Quadratic Forms II (1982).- E. Calabi, Extremal Kähler Metrics (1982).- E. Calabi, Hypersurfaces with Maximal Affinely Invariant Area (1982).- E. Calabi, Extremal Kähler Metrics II (1985).- E. Calabi, Convex Affine Maximal Surfaces (1988).- E. Calabi, Affine Differential Geometry and Holomorphic Curves (1990).- E. Calabi, J. Cao Simple Closed Geodesics on Convex Surfaces (1992).- F. Beukers, J. A. C. Kolk and E. Calabi, Sums of Generalized Harmonic Series and Volumes (1993).- E. Calabi and H. Gluck, What are the Best Almost-Complex Structures on the 6-Sphere? (1993).- E. Calabi, Extremal Isosystolic Metrics for Compact Surfaces (1996).- E. Calabi, P. J. Olver, A. Tannenbaum, Affine Geometry, Curve Flows, and Invariant Numerical Approximations (1996).- J.-P. Bourguignon, E. Calabi, J. Eells, O. Garcia-Prada, M. Gromov, Where Does Geometry Go? A Research and Education Perspective (2001).- E. Calabi, X. Chen, The Space of Kähler Metrics II (2002).- Acknowledgements. </p><p><br></p><p></p><p></p>