On Horizontal Immersions of Discs in Fat Distributions of Type $(4,6)$

Abstract

In this article we discuss horizontal immersions of discs in certain corank-$2$ fat distributions on $6$-dimensional manifolds. The underlying real distribution of a holomorphic contact distribution on a complex $3$ manifold belongs to this class. The main result presented here says that the associated nonlinear PDE is locally invertible. Using this we prove the existence of germs of embedded horizontal discs.

Reorganized and added existence result. To appear in the Journal of Topology and Analysis

References in corpus (2)

• Holomorphic Legendrian curves
• The Oka principle for holomorphic Legendrian curves in ${\mathbb{C}}^{2n+1}$