PREFACE

Recently, by the works of Shoshichi Kobayashi, Takushiro Ochiai, J. Carlson, and P. Griffiths, some of the basic results in complex analysis of one complex variable, such as Schwarz lemma and Nevanlinna theory, have been brought into a new scope and successfully extended to several variables in a very elegant manner. The purpose of this lecture is to give an account of such results. The course was planned for one semester at first, but actually it had to be given separately in two semesters, with a break in-between for half a year. As a result, to the author’s regret the exposition became not so well organized. Nowadays, a tendency prevails to regard the newest results as the most important research sources. However, a glance at those results presented here will give an immediate impression that the contrary is also true in some cases. In fact, except for the elementary prerequisites on complex manifolds, the only background needed here is Nevanlinna’s monograph which was published in 1936. The author expresses his deep gratitude to Mr. Fumio Sakai who dictated the lecture by completing the missing details. (Chapters 1 and 2 were lectured from October 1972 through March 1973 and Chaps. 3 and 4 from October 1973 through March 1974.)