New K\"ahler metric on quasifuchsian space and its curvature properties

Inkang Kim; Xueyuan Wan; Genkai Zhang

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arXiv · 1902.04523

New K\"ahler metric on quasifuchsian space and its curvature properties

Inkang Kim·Xueyuan Wan·Genkai Zhang

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Abstract

Let $QF(S)$ be the quasifuchsian space of a closed surface $S$ of genus $g\geq 2$. We construct a new mapping class group invariant K\"ahler metric on $QF(S)$. It is an extension of the Weil-Petersson metric onthe Teichm\"uller space $\mathcal T(S)\subset QF(S)$. We also calculate its curvature and prove some negativity for the curvature along the tautological directions.

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BibTeX RIS

Inkang Kim, Xueyuan Wan, Genkai Zhang. 2019-02-12. New K\"ahler metric on quasifuchsian space and its curvature properties. https://arxiv.org/abs/1902.04523

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