Some Problems on Differentiable and Complex Manifolds

Abstract

A conference with the title Fiber bundles and differential geometry was held at Cornell University from May 3 to May 7, 1953.* It was supported by a grant from the National Science Foundation. The purpose of the present paper is to record those problems presented at the conference which concern differentiable, almost-complex, complex, and algebraic manifolds. Several of the problems have been solved since the conference. These solutions gave rise to new problems which we will discuss. This report is divided into three sections: differentiable manifolds, almostcomplex manifolds, complex manifolds. The last part contains also the problems on algebraic varieties. Since some problems of the first two sections were motivated by theorems on algebraic varieties, there are occasional references in Sections 1 and 2 to Section 3.1. The author wishes to thank Professors K. Kodaira and D. C. Spencer heartily for many discussions and valuable suggestions during the period of preparation of this report.