The anomaly flow on nilmanifolds

We study the Anomaly flow on 2-step nilmanifolds with respect to any Hermitian connection in the Gauduchon line. In the case of flat holomorphic bundle, the general solution to the Anomaly flow is given for any initial invariant Hermitian metric. The solutions depend on two constants K 1 and K 2 , a...

Full description

Saved in:
Bibliographic Details
Published in:Annals of global analysis and geometry 2021-10, Vol.60 (3), p.501-537
Main Authors: Pujia, Mattia, Ugarte, Luis
Format: Article
Language:English
Subjects:
Analysis
Differential Geometry
Geometry
Global Analysis and Analysis on Manifolds
Invariants
Lie groups
Mathematical Physics
Mathematics
Mathematics and Statistics
String theory
Topology
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We study the Anomaly flow on 2-step nilmanifolds with respect to any Hermitian connection in the Gauduchon line. In the case of flat holomorphic bundle, the general solution to the Anomaly flow is given for any initial invariant Hermitian metric. The solutions depend on two constants K 1 and K 2 , and we study the qualitative behaviour of the Anomaly flow in terms of their signs, as well as the convergence in Gromov–Hausdorff topology. The sign of K 1 is related to the conformal invariant introduced by Fu, Wang and Wu. In the non-flat case, we find the general evolution equations of the Anomaly flow under certain initial assumptions. This allows us to detect non-flat solutions to the Hull-Strominger-Ivanov system on a concrete nilmanifold, which appear as stationary points of the Anomaly flow with respect to the Strominger-Bismut connection.
ISSN:0232-704X
1572-9060
DOI:10.1007/s10455-021-09781-6