On Almost Complex Projective Structures

In the present paper, we shall study an almost complex projective structure which is closely related to the concept of the holomorphically projective change of affine connections. After some preliminaries, in section 2 we introduce the notion of the almost complex projective structure and examine its relationship with affine connections of some type. In section 3, we construct a so-called almost complex projective tangent bundle by giving transition functions in explicit form. Also, it is shown that this bundle is-regarded as an associated bundle of the almost complex projective structure. An exposition of an almost complex projective connection is given in section 4, and section 5 contains a definition of a canonical form on the almost complex projective structure and investigations of some properties concerning it. Finally, the last section is devoted to consideration on a normal connection and the local flatness of the almost complex projective structure. The present auther wishes to express his hearty thanks to Prof. Dr. M. Matsumoto for his kind criticism and encouragement. The auther also wishes to express his sincere thanks to Dr. Y. Ichijyo for his kind instruction.

公開日:2010年1月24日で登録したコンテンツは、国立情報学研究所において電子化したものです。