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Conformally Kähler manifolds*

Published online by Cambridge University Press:  24 October 2008

W. J. Westlake
W. J. Westlake
Affiliation:
37 Sydenham Villas Road Cheltenham
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Extract

Introduction. The present paper is concerned with the conformal geometry of Hermitian spaces. In the first part we find a necessary and sufficient condition for a Hermitian space to be conformally Kähler, that is, conformal to some Kähler space. The condition is that a certain conformal tensor, , vanishes identically. Then, defining a Hermitian manifold as in Hodge (3), we consider such a manifold where the restriction is made that at every point the tensor is zero. This will be called a conformally Kähler manifold, and conditions under which it may be given a Kähler metric are obtained. It is found that any conformally Kähler manifold may be given a Kähler metric provided it is simply-connected or that its fundamental group is of finite order.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 50 , Issue 1 , January 1954 , pp. 16 - 19
Copyright
Copyright © Cambridge Philosophical Society 1954

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References

REFERENCES

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