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Remarks on k-Leviflat Complex Manifolds

Published online by Cambridge University Press:  20 November 2018

B. Gilligan  and
A. Huckleberry
B. Gilligan
Affiliation:
University of Regina, Regina, Saskatchewan
A. Huckleberry
Affiliation:
University of Notre Dame, Notre Dame, Indiana
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In the theory of functions of several complex variables one is naturally led to study non-compact complex manifolds which have certain types of exhaustions. For example, on a Stein manifold X there is a strictly plurisubharmonic function ϕ: X → R+ so that the pseudoballs Bc = {φ < c } exhaust X. Conversely, a manifold which has such an exhaustion is Stein. The purpose of this note is to study a class of manifolds which have exhaustions along the lines of those on holomorphically convex manifolds, namely the k-Leviflat complex manifolds. Unlike the Stein case, the Levi form may have positive dimensional 0-eigenspaces. In the holomorphically convex case these are tangent to the generic fiber of the Remmert reduction.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 31 , Issue 4 , 01 August 1979 , pp. 881 - 889
Copyright
Copyright © Canadian Mathematical Society 1979

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