Page 2 - Curvature and Homology

CURVATURE

AND

HOMOLOGY

Revised Edition

Samuel I. Goldberg

Mathematicians interested in the curvature properties of Riemannian mani-
folds and their homologic structures, an increasingly important and
specialized branch of differential geometry, will welcome this excellent
teaching text. Revised and expanded by its well-known author, this volume
offers a systematic and self-contained treatment of subjects such as the topol-
ogy of differentiate manifolds, curvature and homology of Riemannian man-
ifolds, compact Lie groups, complex manifolds, and the curvature and
homology of Kaehler manifolds.

In addition to a new preface, this edition includes five new appendices con-
cerning holomorphic bisectional curvature, the Gauss-Bonnet theorem, some
applications of the generalized Gauss-Bonnet theorem, an application of
Bochners lemma, and the Kodaira vanishing theorems. Geared toward readers
familiar with standard courses in linear algebra, real and complex variables,
differential equations, and point-set topology, the book features helpful exer-
cises at the end of each chapter that supplement and clarify the text.

This lucid and thorough treatment—hailed by Nature magazine as ".. . a
valuable survey of recent work and of probable lines of future progress"—
includes material unavailable elsewhere and provides an excellent resource
for both students and teachers.
Unabridged Dover (1998) corrected republication of the work originally pub-
lished by Academic Press, New York, 1962. New Preface. Introduction. Five
new appendixes. Bibliography. Indices. 416pp. 5 3/8 x 8 1/2 Paperbound.
Free Dover Mathematics and Science Catalog (59065-8) available upon
request.