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

Divakaran Divakaran; Dheeraj Kulkarni

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

Differential Geometry 2018-07-24 v3 Algebraic Geometry Complex Variables Dynamical Systems Symplectic Geometry

Authors: Divakaran Divakaran , Dheeraj Kulkarni

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 $\mathbb{CP}^2$ .

Keywords

riemann surface lamination cp^2 asymptotically holomorphic totally geodesic fubini-study metric minimal exceptional sets

Cite

@article{arxiv.1805.10862,
  title  = {On the existence of non-trivial laminations in $\mathbb{CP}^2$},
  author = {Divakaran Divakaran and Dheeraj Kulkarni},
  journal= {arXiv preprint arXiv:1805.10862},
  year   = {2018}
}

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

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

Abstract

Keywords

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