Geometric approach to the Weil-Petersson symplectic form

Reynir Axelsson*, Georg Schumacher

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In a family of compact, canonically polarized, complex manifolds the first variation of the lengths of closed geodesics is computed. As an application, we show the coincidence of the Fenchel-Nielsen and Weil-Petersson symplectic forms on the Teichmüller spaces of compact Riemann surfaces in a purely geometric way. The method can also be applied to situations like moduli spaces of weighted punctured Riemann surfaces, where the methods of Kleinian groups are not available.

Original languageEnglish
Pages (from-to)243-257
Number of pages15
JournalCommentarii Mathematici Helvetici
Issue number2
Publication statusPublished - 2010

Other keywords

  • Fenchel-Nielsen coordinates
  • Symplectic geometry
  • Weil-Petersson form


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