We prove that the space of convex real projective structures on a surface of genus $g \geq 2$ admits a mapping class group invariant Kähler metric where Teichmüller space with Weil–Petersson metric is a totally geodesic complex submanifold.
Research partially supported by STINT-NRF grant (2011-0031291). Research by G.
Zhang is supported partially by the Swedish Science Council (VR). I. Kim
gratefully acknowledges the partial support of grant (NRF-2017R1A2A2A05001002)
and a warm support of Chalmers University of Technology during his stay.
"Kähler metric on the space of convex real projective structures on surface." J. Differential Geom. 106 (1) 127 - 137, April 2017. https://doi.org/10.4310/jdg/1493172095