A Hermitian metric on a complex manifold is Kähler if and only if it approximates the Euclidean metric to order 2 at each point, in a suitable coordinate system. We prove here an analogous characterization of balanced metrics, namely, a Hermitian metric is balanced if and only if its fundamental form ω has closed trace and ωi, j (z) does not contain linear terms involving zi , z j , \bar zi , \bar z j , for each point, in a suitable coordinate system.

A characterization of balanced manifolds / Alessandrini, Lucia. - In: COMPTES RENDUS MATHÉMATIQUE. - ISSN 1631-073X. - 352:4(2014), pp. 345-350. [10.1016/j.crma.2014.02.004]

A characterization of balanced manifolds

ALESSANDRINI, Lucia
2014-01-01

Abstract

A Hermitian metric on a complex manifold is Kähler if and only if it approximates the Euclidean metric to order 2 at each point, in a suitable coordinate system. We prove here an analogous characterization of balanced metrics, namely, a Hermitian metric is balanced if and only if its fundamental form ω has closed trace and ωi, j (z) does not contain linear terms involving zi , z j , \bar zi , \bar z j , for each point, in a suitable coordinate system.
2014
A characterization of balanced manifolds / Alessandrini, Lucia. - In: COMPTES RENDUS MATHÉMATIQUE. - ISSN 1631-073X. - 352:4(2014), pp. 345-350. [10.1016/j.crma.2014.02.004]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/2665062
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