Timeline for Metric associated to a Connection on a Vector Bundle

9 events

when toggle format	what		by	license	comment
Apr 13, 2017 at 12:58	history	edited	CommunityBot		replaced http://mathoverflow.net/ with https://mathoverflow.net/
Mar 26, 2012 at 12:30	vote	accept	Giovanni De Gaetano
Mar 19, 2012 at 16:38	answer	added	YangMills		timeline score: 6
Mar 19, 2012 at 15:41	history	edited	Giovanni De Gaetano	CC BY-SA 3.0	added 228 characters in body
Mar 19, 2012 at 15:38	comment	added	Giovanni De Gaetano		I´m really sorry for the delay in the response. You are totally right! Indeed I´m looking for an Hermitian structure on $L$ which is harmonic (i.e. the form $\Delta log \\| s\\|dxdy$ is identically zero for a rational sections $s$ of $L$, so for every rational section). I´m going to edit the question right now.
Mar 19, 2012 at 15:11	vote	accept	Giovanni De Gaetano
Mar 26, 2012 at 12:30
Mar 9, 2012 at 16:18	comment	added	David E Speyer		The construction which I am aware of takes as input a complex manifold $M$, a holomorphic vector bundle $E$, and a smooth Hermitian structure on $E$, and returns a unique connection (the Chern connection) which is compatible with these. You are implying that there is a construction whose input is a a complex manifold $M$, a holomorphic vector bundle $E$, and a Hermitian metric on $M$. Did you mean to ask for the Hermitian structure to be on $E$, or is the "metric connection" something other than the Chern connection?
Mar 9, 2012 at 16:03	answer	added	alvarezpaiva		timeline score: 6
Mar 9, 2012 at 15:25	history	asked	Giovanni De Gaetano	CC BY-SA 3.0