Page 5 - Curvature and Homology

PREFACE TO THE ENLARGED EDITION
Originally, in the first edition of this work, it was the author's purpose
to provide a self-contained treatment of Curvature and Homology. Sub-
sequently, it became apparent that the more important applications are
to Kaehler manifolds, particularly the Kodaira vanishing theorems,
which appear in Chapter VI. To make this chapter comprehensible,
Appendices F and I have been added to this new edition. In these Appen-
dices, the Chern classes are defined and the Euler characteristic is given
by the Gauss-Bonnet formula-the latter being applied in Appendix G.
Several important recent developments are presented in Appendices E
and H. In Appendix E, the differential geometric technique due to
Bochner gives rise to an important result that was established by Siu and
Yau in 1980. The same method is applied in Appendix H to F-structures
over negatively curved spaces.
S. I. GOLDBERG
Urbana, Illinois
February, 1998