Homogeneous Lagrangian foliations on complex space forms

TL;DR

This paper classifies holomorphic isometric actions on complex space forms with Lagrangian orbits, identifying specific foliations in Euclidean and hyperbolic spaces, advancing understanding of geometric structures in complex differential geometry.

Contribution

It provides a complete classification of such actions, revealing that only Lagrangian affine and horocycle foliations occur in these settings.

Findings

Lagrangian affine subspace foliations in complex Euclidean spaces

Lagrangian horocycle foliations in complex hyperbolic spaces

Classification is up to orbit equivalence

Abstract

We classify holomorphic isometric actions on complex space forms all whose orbits are Lagrangian submanifolds, up to orbit equivalence. The only examples are Lagrangian affine subspace foliations of complex Euclidean spaces, and Lagrangian horocycle foliations of complex hyperbolic spaces.