Abstract
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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
