Lower order tensors in non-K\"ahler geometry and non-K\"ahler geometric flow

TL;DR

This paper classifies second order curvature flows in non-K"ahler geometries by analyzing lower order tensors, providing a unified framework inspired by Streets and Tian's curvature flows.

Contribution

It introduces a systematic method to construct and classify second order curvature flows in various non-K"ahler geometries based on tensor classification.

Findings

Unified classification of second order curvature flows

Framework applicable to almost Hermitian, almost K"ahler, and Hermitian geometries

Provides insights into the structure of non-K"ahler geometric flows

Abstract

In recent years, Streets and Tian introduced a series of curvature flows to study non-K\"{a}hler geometry. In this paper, we study how to construct second order curvature flows in a uniform way, under some natural assumptions which holds in Streets and Tian's works. As a result, by classifying the lower order tensors, we classify the second order curvature flows in almost Hermitian, almost K\"{a}hler and Hermitian geometries in certain sense.