Cheng S.Y., Li P., Tian G. (eds.) A Mathematician and His Mathematical Work: Selected Papers of S.S. Chern

World Scientific, 1996. — 707 p.This volume is about the life and work of Shiing-Shen Chern (1911–2004), one of the leading mathematicians of this century. The book contains personal accounts by some friends, together with a summary of the mathematical works by Chern himself. Besides a selection of the mathematical papers the book also contains all his papers published after 1988.
Professor Chern is regarded as the greatest geometer of his generation. For six decades, he has been a leader in the field of differential geometry. Professor Chern has extremely broad interests and has made seminal contributions to such diverse areas as web geometry, integral geometry, complex manifolds, minimal submanifolds and characteristics classes.Foreword.
The Life and Mathematics of Shiing-Shen Chern (by R. S. Palais, C.-L. Terng).
My Mathematical Education (by S. S. Chern).
A Summary of My Scientific Life and Works (by S. S. Chern).
S. S. Chern as Geometer and Friend (by A. Weil).
Some Reflections on the Mathematical Contributions of S. S. Chern (by P. A. Griffiths).
Shiing-Shen Chern as Friend and Mathematician (by W.-L. Chow).
Papers Published in 1932-1987
Abzahlungen fur Gewebe // Abh. Math. Sem. Univ. Hamburg 11 (1935) 163-170.
On Integral Geometry in Klein Spaces // Ann. of Math. 43 (1942) 178-189.
A Simple Intrinsic Proof of the Gauss-Bonnet Formula for Closed Riemannian Manifolds // Ann. of Math. 45 (1944) 747-752.
On the Curvature Integra in a Riemannian Manifold // Ann. of Math. 46 (1945) 674-684.
Characteristic Classes of Hermitian Manifolds // Ann. of Math. 47 (1946) 85-121.
Sur une Classe Remarquable de Varietes dans l'espace Projectif a N Dimensions // Science Reports Nat. Tsing Hua Univ. 4 (1947) 328-336.
(with E. Spanier) A Theorem on Orientable Surfaces in Four-Dimensional Space // Comm. Math. Helv. 25 (1951) 205-209.
On the Kinematic Formula in the Euclidean Space of N Dimensions // Amer. J. Math 74 (1952) 227-236.
On a Generalization of Kahler Geometry // Lefschetz jubilee volume. Princeton Univ. Press (1957) 103-121.
(with R. K. Lashof) On the Total Curvature of Immersed Manifolds // Amer. J. of Math. 79 (1957) 306-318.
(with F. Hirzebruch, J. P. Serre) On the Index of a Fibered Manifold // Proc. Amer. Math. Soc. 8 (1957) 587-596.
(with R. K. Lashof) On the Total Curvature of Immersed Manifolds, II // Michigan Math. J. 5 (1958) 5-12.
Integral Formulas for Hypersurfaces in Euclidean Space and Their Applications to Uniqueness Theorems // J. of Math, and Mech. 8 (1959) 947-956.
(with J. Hano, C. C. Hsiung) A Uniqueness Theorem on Closed Convex Hypersurfaces in Euclidean Space // J. of Math. and Mech. 9 (1960) 85-88.
The Integrated Form of the First Main Theorem for Complex Analytic Mappings in Several Complex Variables // Ann. of Math. 71 (1960) 536-551.
(with R. Bott) Hermitian Vector Bundles and the Equidistribution of the Zeroes of Their Holomorphic Sections // Acta. Math. 114 (1965) 71-112.
On the Kinematic Formula in Integral Geometry // J. of Math. and Mech. 16 (1966) 101-118.
(with H. I. Levine, L. Nirenberg) Intrinsic Norms on a Complex Manifold // Global analysis, Princeton Univ. Press (1970) 119-139.
(with R. Bott) Some Formulas Related to Complex Transgression // Essays on Topology and Related Topics, Springer-Verlag (1970) 48-57.
(with J. Simons) Characteristic Forms and Geometric Invariants // Ann. of Math. 99 (1974) 48-69.
(with J. K. Moser) Real Hypersurfaces in Complex Manifolds // Acta. Math. 133 (1974) 219-271.
(with C.-L. Terng) An Analogue of Backlund's Theorem in Affine Geometry // Rocky Mountain J. Math. 10 (1979) 105-124.
From Triangles to Manifolds // Amer. Math. Monthly 86 (1979) 339-349.
(with C.-K. Peng) Lie Groups and KdV Equations // Manuscripta Math. 28 (1979) 207-217.
Deformation of Surfaces Preserving Principal Curvatures // Differential Geometry and Complex Analysis, Volume in Memory of H. Rauch, Springer-Verlag (1984) 155-163.
Papers Published Since 1988
(with T. Cecil) Dupin Submanifolds in Lie Sphere Geometry // Differential Geometry and Topology, Springer Lecture Notes, No. 1369, 1-48.
Historical Remarks on Gauss-Bonnet // Analysis, et cetera. Volume in Honor of Jurgen Moser, Academic Press (1990) 209-217.
What is Geometry? // Amer. Math. Monthly 97 (1990) 678-686.
An Introduction to Dupin Submanifolds // Differential Geometry, A Symposium in Honor of M. do Carmo, Longman (1991) 95-102.
Families of Hypersurfaces under Contact Transformations in Rⁿ // International Symposium in Memory of Hua Loo Keng, Springer (1991) 49-56.
Surface Theory with Darboux and Bianchi // Miscellanea Mathematica, Volume Dedicated to H. Gotze, Springer (1991) 59-69.
Transgression in Associated Bundles // Internal. J. Math. 2 (1991) 383-393.
Characteristic Classes and Characteristic Forms // Paul Halmos Celebrating 50 Years of Math., Springer, 169-177.
On Finsler Geometry // Comptes Rendus Sci., Paris 314 (1992) 757-761.
Yang-Mills Equations and Yang-Baxter Equations // Chinese J. of Phys., Yang Volume, Taiwan Physical Society 30 (1992) 949-953.
(with D. Bao) On a Notable Connection in Finsler Geometry // Houston J. Math. 19 (1993) 135-180.
Characteristic Classes as a Geometric Object // Global Analysis in Modern Mathematics (Palais Festival Volume), Publish or Perish, 221-226.
Sophus Lie and Differential Geometry // The Sophus Lie Memorial Conference, Oslo 1992 Proceedings, 129-137.
(with S. Y. Ji) Projective Geometry and Riemann's Mapping Problem // Mathematische Annalen 302 (1995) 581-600.
Shiing-Shen Chern Curriculum Vitae.
List of Ph.D. Theses Written Under the Supervision of S. S. Chern.
Bibliography of the Publications of S. S. Chern.