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Mathematics > Differential Geometry

arXiv:1805.10862 (math)
[Submitted on 28 May 2018 (v1), last revised 23 Jul 2018 (this version, v3)]

Title:On the existence of non-trivial laminations in $\mathbb{CP}^2$

Authors:Divakaran Divakaran, Dheeraj Kulkarni
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Abstract:In this article, we show the existence of a nontrivial Riemann surface lamination embedded in $\mathbb{CP}^2$ by using Donaldson's construction of asymptotically holomorphic submanifolds. Further, the lamination we obtain has the property that each leaf is a totally geodesic submanifold of $\mathbb{CP}^2 $ with respect to the Fubini-Study metric. This may constitute a step in understanding the conjecture on the existence of minimal exceptional sets in $\mathbb{CP}^2$.
Comments: Caution: There is an error in the argument (thanks to E. Ghys for pointing it out). We believe that it can be fixed and article will be updated soon with a correct argument. We thank you for your patience
Subjects: Differential Geometry (math.DG); Algebraic Geometry (math.AG); Complex Variables (math.CV); Dynamical Systems (math.DS); Symplectic Geometry (math.SG)
MSC classes: 37F75, 57R30, 57R15, 53C56, 53C12
Cite as: arXiv:1805.10862 [math.DG]
  (or arXiv:1805.10862v3 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.1805.10862

Submission history

From: Dheeraj Kulkarni [view email]
[v1] Mon, 28 May 2018 10:49:06 UTC (153 KB)
[v2] Sun, 15 Jul 2018 13:51:34 UTC (17 KB)
[v3] Mon, 23 Jul 2018 06:55:04 UTC (17 KB)
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