Hermitian curvature flow | Zendy

Jeffrey Streets | Zendy; Gang Tian | Zendy

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Hermitian curvature flow

Author(s) -

Jeffrey Streets,

Gang Tian

Publication year - 2011

Publication title -

journal of the european mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.549

H-Index - 64

eISSN - 1435-9863

pISSN - 1435-9855

DOI - 10.4171/jems/262

Subject(s) - mathematics , hermitian matrix , curvature , flow (mathematics) , connection (principal bundle) , einstein , mathematical analysis , elliptic curve , euler equations , chern class , pure mathematics , mathematical physics , geometry

We define a functional for Hermitian metrics using the curvature of the Chernconnection. The Euler-Lagrange equation for this functional is an ellipticequation for Hermitian metrics. Solutions to this equation are related toK\"ahler-Einstein metrics, and are automatically K\"ahler-Einstein undercertain conditions. Given this, a natural parabolic flow equation arises. Weprove short time existence and regularity results for this flow, as well asstability for the flow near K\"ahler-Einstein metrics with negative or zerofirst Chern class.

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