# Remarks on complex contact manifolds

@inproceedings{Kobayashi1959RemarksOC,
title={Remarks on complex contact manifolds},
author={Sh{\^o}shichi Kobayashi},
year={1959}
}
1. Statement of results. Let M be a complex manifold of complex dimension 2n+1. Let { Ui} be an open covering of M. We call M a complex contact manifold if the following conditions are satisfied: (1) On each Ui there exists a holomorphic 1-form coi such that ciA(dci)" is different from zero at every point of U;. (2) If U,\ Us is nonempty, then there exists a nonvanishing holomorphic function f;q on U;C US such that cow =f,wj on Ui; Us. We shall prove the following

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## References

SHOWING 1-6 OF 6 REFERENCES

### SOME GLOBAL PROPERTIES OF CONTACT STRUCTURES

transformations in general and to the study of global contact transformations in the special case of euclidean space. In attempting to generalize Lie's results to more general manifolds, it becomes

### Theory of Lie Groups

This famous book was the first treatise on Lie groups in which a modern point of view was adopted systematically, namely, that a continuous group can be regarded as a global object. To develop this

### Theory of Lie Groups

IN recent years great advances have been made in our knowledge of the fundamental structures of analysis, particularly of algebra and topology, and an exposition of Lie groups from the modern point

• J. Math. vol
• 1958

### Pseudo-groupes continus infinis

• Colloque de Geome'trie Diff.,
• 1953