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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Affine connections and defining functions of real hypersurfaces in $ {\bf C}\sp{n}$


Author: Hing Sun Luk
Journal: Trans. Amer. Math. Soc. 259 (1980), 579-588
MSC: Primary 53C05; Secondary 32F25, 53B05
MathSciNet review: 567098
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Abstract: The affine connection and curvature introduced by Tanaka on a strongly pseudoconvex real hypersurface are computed explicitly in terms of its defining function. If Fefferman's defining function is used, then the Ricci form is shown to be a function multiple of the Levi form. The factor is computable by Fefferman's algorithm and its positivity implies the vanishing of certain cohomology groups (of the $ {\bar \partial _b}$ complex) in the compact case.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1980-0567098-3
PII: S 0002-9947(1980)0567098-3
Keywords: Strongly pseudoconvex real hypersurface, affine connection, Ricci operator, defining function, Levi form, boundary Laplacian
Article copyright: © Copyright 1980 American Mathematical Society