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A geometric flow of Balanced metrics Vezzoni, Luigi
Description
An Hermitian metric $g$ on a complex manifold $M$ is called {\em balanced} if its fundamental form $\omega$ is co-closed. Typically examples of balanced manifolds are given by modifications of K\"ahler manifolds, twistor spaces over anti-self-dual oriented Riemannian $4$-manifolds and nilmanifolds. In the talk it will be discussed a geometric flow of balanced metrics. The flow was introduced in \cite{BFV1} and consists in a generalisation of the Calabi flow to the balanced context. The flow preserves the Bott-Chern cohomology class of the initial metric and in the K\"ahler case reduces to the classical Calabi flow. It will be showed that the flow is well-posedn and stable around Ricci flat K\"ahler metrics. Furthermore, the talk focuses on a rencent problem in balanced geometry proposed in \cite{FV}. \begin{thebibliography}{12} \bibitem{BFV1} {\sc L. Bedulli, L. Vezzoni}, A parabolic flow of balanced metrics. {\em Journal f\"ur die reine und angewandte Mathematik (Crelle)}. {\bf 723} (2017), 79--99. \bibitem{BFV2} {\sc L.~Bedulli and L. Vezzoni}, A scalar Calabi-type flow in Hermitian Geometry, to appear in {\em Ann. Sc. Norm. Super. Pisa Cl. Sci. (5)}. \bibitem{BFV3} {\sc L.~Bedulli and L. Vezzoni}, Stability of geometric flows of closed forms. {\tt\, arXiv:1811.09416}. \bibitem{FGV} {\sc A. Fino, G. Grantcharov, L. Vezzoni}, Astheno-K\"ahler and balanced structures on fibrations. {\tt arXiv:1608.06743}, to appear in {\em IMRN}. \bibitem{FV} {\sc A. Fino, L. Vezzoni,} Special Hermitian metrics on compact solvmanifolds, {\em J. Geom. Phys.} {\bf 91} (Special Issue) (2015), 40--53. \end{thebibliography}
Item Metadata
Title |
A geometric flow of Balanced metrics
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2019-10-31T15:40
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Description |
An Hermitian metric $g$ on a complex manifold $M$ is called {\em balanced} if its fundamental form $\omega$ is co-closed. Typically
examples of balanced manifolds are given by modifications of K\"ahler manifolds, twistor spaces over anti-self-dual oriented Riemannian $4$-manifolds and nilmanifolds. In the talk it will be discussed a geometric flow of balanced metrics. The flow was introduced in \cite{BFV1} and consists in a generalisation of the Calabi flow to the balanced context. The flow preserves the Bott-Chern cohomology class of the initial metric and in the K\"ahler case reduces to the classical Calabi flow.
It will be showed that the flow is well-posedn and stable around Ricci flat K\"ahler metrics. Furthermore, the talk focuses on a rencent problem in balanced geometry proposed in \cite{FV}.
\begin{thebibliography}{12}
\bibitem{BFV1}
{\sc L. Bedulli, L. Vezzoni}, A parabolic flow of balanced metrics.
{\em Journal f\"ur die reine und angewandte Mathematik (Crelle)}. {\bf 723} (2017), 79--99.
\bibitem{BFV2} {\sc L.~Bedulli and L. Vezzoni}, A scalar Calabi-type flow in Hermitian Geometry, to appear in {\em Ann. Sc. Norm. Super. Pisa Cl. Sci. (5)}.
\bibitem{BFV3} {\sc L.~Bedulli and L. Vezzoni}, Stability of geometric flows of closed forms. {\tt\, arXiv:1811.09416}.
\bibitem{FGV}
{\sc A. Fino, G. Grantcharov, L. Vezzoni}, Astheno-K\"ahler and balanced structures on fibrations. {\tt arXiv:1608.06743}, to appear in {\em IMRN}.
\bibitem{FV}
{\sc A. Fino, L. Vezzoni,}
Special Hermitian metrics on compact solvmanifolds, {\em J. Geom. Phys.} {\bf 91} (Special Issue) (2015), 40--53.
\end{thebibliography}
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Extent |
54.0 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: University of Torino
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Series | |
Date Available |
2020-04-29
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0390031
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Researcher
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International