Curvature of new Kähler metrics on the total space of Griffiths negative vector bundle and quasi-Fuchsian space

Abstract

We study Kähler metrics on the total space of Griffiths negative holomorphic vector bundles over Kähler manifolds. As an application, we construct mapping class group invariant Kähler metrics on [Formula: see text], the holomorphic tangent bundle of Teichmüller space of a closed surface [Formula: see text]. Consequently,we obtain a new mapping class group invariant Kähler metric on the quasi-Fuchsian space [Formula: see text], which extends the Weil–Petersson metric on the Teichmüller space [Formula: see text]. We also calculate its curvature and prove non-positivity for the curvature along the tautological directions.