Handbook of Differential Geometry, Volume 1

In the series of volumes which together will constitute the Handbook of Differential Geometry a rather complete survey of the field of differential geometry is given. The different chapters will both deal with the basic material of differential geometry and with research results (old and recent). All chapters are written by experts in the area and contain a large bibliography.

Preface. Introduction (S.S. Chern). List of Contributors. Differential geometry of webs (M.A. Akivis, V.V. Goldberg). Spaces of metrics and curvature functionals (D.E. Blair). Riemannian Submanifolds (B.-Y. Chen). Einstein metrics in dimension four (A. Derdzinski). The Atiyah-Singer Index Theorem (P.B. Gilkey). Survey of isospectral manifolds (C.S. Gordon). Submanifolds with parallel fundamental form (Ü. Lumiste). Sphere theorems (K. Shiohama). Affine differential geometry (U. Simon). A survey on isoparametric hypersurfaces and their generalizations (G. Thorbergsson). Curves (T. Willmore). Author Index. Subject Index.