ID  26 
Author 
Ichijyo, Yoshihiro
College of General Education Tokushima University

Content Type 
Departmental Bulletin Paper

Description  The theory of real projective connections standing on the viewpoint of the theory of vector bundles was investigated perfectly by T. Otsuki. Its extension to generalized spaces was done by the present author and K. Eguchi. On the other hand, T. Ishihara studied complex projective structures and found the close relation between the complex projective structures and Hprojective connections which had been introduced by T. Tashiro and developed by S. Ishihara and many other authors. In the present paper, our main purpose is to study manifolds endowed with almost complex projective structures. First of all, in §§1 and 2, we consider an almost complex projective vector bundle introduced in [4] and several distributions which define an almost complex projective connection. This connection, however, can be determined also by an usual differential geometric method. In §3, we find a certain distribution P which is intrinsic to the almost complex projective connection. A mapping σ which gives a correspondence between any two fibers in the almost complex projective vector bundle is treated in §4. And we show that the mapping σ preserves the complex projective structure in each fiber invariant if the distribution P is integrable. The last section is devoted to study a manifold where the given distribution P is integrable, for example, we obtain that if P is integrable then the manifold is an Hprojectively flat complex manifold.

Journal Title 
Journal of mathematics, Tokushima University

ISSN  00754293

NCID  AA00701816

Volume  6

Start Page  1

End Page  15

Sort Key  1

Published Date  1972

Remark  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。

FullText File  
language 
eng
