Transverse Fully Nonlinear Equations on Sasakian Manifolds and Applications

TL;DR

This paper establishes a priori estimates for transverse fully nonlinear equations on Sasakian manifolds, leading to geometric applications like transverse Calabi-Yau theorems for various metrics, with extensions to Hermitian foliated manifolds.

Contribution

It introduces new a priori estimates for nonlinear equations on Sasakian manifolds and extends these results to transverse Hermitian foliated manifolds, enabling new geometric theorems.

Findings

Proved a priori estimates for transverse fully nonlinear equations.

Established transverse Calabi-Yau theorems for specific metrics.

Extended results to compact oriented, taut, transverse Hermitian foliated manifolds.

Abstract

We prove a priori estimates for a class of transverse fully nonlinear equations on Sasakian manifolds and give some geometric applications such as the transversion Calabi-Yau theorem for transverse balanced and (strongly) Gauduchon metrics. We also explain that similar results hold on compact oriented, taut, transverse Hermitian foliated manifold of complex co-dimension $n$, and give some geometric applications such as the transverse Calabi-Yau theorems for transverse Hermitian and (strongly) Gauduchon metrics.