On some variational problems for 2-dimensional Hermitian metrics

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Let (M, J, g) be a compact complex 2-dimensional Hermitian manifold with the Kähler form Ω, and the torsion 1-form ω defined by dΩ = ω ∧ Ω. In this note we obtain the Euler-Lagrange equations for the variational functionals defined by {norm of matrix}ω{norm of matrix}2 and {norm of matrix}dω{norm of matrix}2, where g runs in the space of all the Hermitian metrics on M. In the first case, the extremals are precisely the Kähler metrics [Gd]. In the second case, we also write down a formula for the second variation.

Original languageEnglish
Pages (from-to)137-145
Number of pages9
JournalAnnals of Global Analysis and Geometry
Issue number2
StatePublished - Jan 1990

ASJC Scopus subject areas

  • Analysis
  • Political Science and International Relations
  • Geometry and Topology


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