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Some deformations of the Hopf foliation are also Kähler


Author: Paul D. Scofield
Journal: Proc. Amer. Math. Soc. 119 (1993), 251-253
MSC: Primary 53C12; Secondary 32G08, 32L30, 53C55
DOI: https://doi.org/10.1090/S0002-9939-1993-1143225-9
MathSciNet review: 1143225
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Abstract: Fix $ \alpha = ({\alpha _0}, \ldots ,{\alpha _n}) \in \ring{\mathbf{R}}^{n + 1}$. The trajectories of the flow on $ {{\mathbf{S}}^{2n + 1}} \subset {{\mathbf{C}}^{n + 1}}$ given by

$\displaystyle {\phi _t}:({z_0}, \ldots ,{z_n}) \mapsto ({z_0}{e^{i{\alpha _0}t}}, \ldots ,{z_n}{e^{i{\alpha _n}t}})$

constitute the leaves of a $ 2n$-codimensional (nonsingular) foliation of $ {{\mathbf{S}}^{2n + 1}}$. We use (locally defined) branches of the logarithm to give this foliation a (global) transverse Kähler structure.

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

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1143225-9
Keywords: Hopf foliation, transverse Kähler foliation
Article copyright: © Copyright 1993 American Mathematical Society