New curvature flows in complex geometry
type: Item
instance of: scholarly article
title: New curvature flows in complex geometry
zbMATH Open document ID: 1408.32027
author: D. H. Phong
author: Sebastien Picard
author: Xiangwen Zhang
publication date: 2018-12-19T00:00:00Z
full work available at URL: https://arxiv.org/abs/1806.11235
review text: The Kähler condition is a condition on \((1,1)\)-forms. If one has to implement a condition weaker than it, one faces as obstacle the absence of a \(\partial \bar{\partial}\)-Lemma in non-Kähler geometry. In such a context arises the anomaly flow which is a flow on \((2,2)\)-forms on a \(3\)-dimensional complex manifold and a generalization of the Ricci flow. The paper is a survey of what is known about this and other known curvature flows in non-Kähler geometry and in the theory of non-linear partial differential equations. For the entire collection see [Zbl 1402.14006].
Mathematics Subject Classification ID: 32Q99
Mathematics Subject Classification ID: 53C99
Mathematics Subject Classification ID: 32-02
Mathematics Subject Classification ID: 53-02
zbMATH DE Number: 6996018
zbMATH Keywords: Ricci flow
zbMATH Keywords: anomaly flow
zbMATH Keywords: (non-)Kähler geometry
reviewed by: Vladimir P. Kostov
MaRDI profile type: Publication
Wikidata QID: Q115160777
arXiv ID: 1806.11235
OpenAlex ID: W2962804040
DOI: 10.4310/SDG.2017.V22.N1.A13
description: scientific article