Communications in Analysis and Geometry

Volume 27 (2019)

Number 3

Differential geometry of the mixed Hodge metric

Pages: 671 – 742



Gregory Pearlstein (Department of Mathematics, Texas A&M University, College Station, Tx., U.S.A.)

Chris Peters (Faculteit Wiskunde en Informatica, Eindhoven University of Technology, The Netherlands)


We investigate properties of the mixed Hodge metric of a mixed period domain. In particular, we calculate its curvature and the curvature of the Hodge bundles. We also consider when the pull back metric via a period map is Kähler. Several applications in cases of geometric interest are given, such as for normal functions and biextension bundles.

Received 20 July 2016

Accepted 17 March 2017

Published 3 September 2019