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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.

References [Enhancements On Off] (What's this?)

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Keywords: Strongly pseudoconvex real hypersurface, affine connection, Ricci operator, defining function, Levi form, boundary Laplacian
Article copyright: © Copyright 1980 American Mathematical Society