Some deformations of the Hopf foliation are also Kähler
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- by Paul D. Scofield PDF
- Proc. Amer. Math. Soc. 119 (1993), 251-253 Request permission
Abstract:
Fix $\alpha = ({\alpha _0}, \ldots ,{\alpha _n}) \in \mathring {\mathbf {R}}^{n + 1}$. The trajectories of the flow on ${{\mathbf {S}}^{2n + 1}} \subset {{\mathbf {C}}^{n + 1}}$ given by \[ {\phi _t}:({z_0}, \ldots ,{z_n}) \mapsto ({z_0}{e^{i{\alpha _0}t}}, \ldots ,{z_n}{e^{i{\alpha _n}t}})\] 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
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Additional Information
- © Copyright 1993 American Mathematical Society
- 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