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Differential forms on a Kähler manifold

Published online by Cambridge University Press:  24 October 2008

W. V. D. Hodge
W. V. D. Hodge
Affiliation:
Pembroke CollegeCambridge
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Extract

While a number of special properties of differential forms on a Kähler manifold have been mentioned in the literature on complex manifolds, no systematic account has yet been given of the theory of differential forms on a compact Kähler manifold. The purpose of this paper is to show how a general theory of these forms can be developed. It follows the general plan of de Rham's paper (2) on differential forms on real manifolds, and frequent use will be made of results contained in that paper. For convenience we begin by giving a brief account of the theory of complex tensors on a complex manifold, and of the differential geometry associated with a Hermitian, and in particular a Kählerian, metric on such a manifold.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 47 , Issue 3 , July 1951 , pp. 504 - 517
Copyright
Copyright © Cambridge Philosophical Society 1951

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References

REFERENCES

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(3)de Rham, G. and Kodaira, K.Lectures on harmonic forms delivered at the Institute for Advanced Studies (Princeton, 1950).Google Scholar
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