標題: The Velling-Kirillov metric on the universal Teichmuller curve
作者: Teo, LP
應用數學系
Department of Applied Mathematics
公開日期: 2004
摘要: We extend Velling's approach and prove that the second variation of the spherical areas of a family of domains defines a Hermitian metric on the universal Teichmuller curve, whose pull-back to Diff +(S-1)/S-1 coincides with the Kirillov metric. We call this Hermitian metric the Velling-Kirillov metric. We show that the vertical integration of the square of the symplectic form of the Veiling-Kirillov metric on the universal Teichmuller curve is the symplectic form that defines the Weil-Petersson metric on the universal Teichmuller space. Restricted to a finite dimensional Teichmuller space, the vertical integration of the corresponding form on the Teichmuller curve is also the symplectic form that defines the Weil-Petersson metric on the Teichmuller space.
URI: http://hdl.handle.net/11536/27260
http://dx.doi.org/10.1007/BF02789310
ISSN: 0021-7670
DOI: 10.1007/BF02789310
期刊: JOURNAL D ANALYSE MATHEMATIQUE
Volume: 93
起始頁: 271
結束頁: 307
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