Let f : Y → X be a continuous map between a compact real analytic Kähler manifold (Y, g) and a compact complex hyperbolic manifold (X, g0). In this paper we give a lower bound of the diastatic entropy of (Y, g) in terms of the diastatic entropy of (X, g0) and the degree of f . When the lower bound is attained we get geometric rigidity theorems for the diastatic entropy analogous to the ones obtained by G. Besson, G. Courtois and S. Gallot [2] for the volume entropy. As a corollary,when X = Y,we get that the minimal diastatic entropy is achieved if and only if g is isometric to the hyperbolic metric g0.
@article{bwmeta1.element.doi-10_1515_coma-2016-0006,
author = {Roberto Mossa},
title = {Diastatic entropy and rigidity of complex hyperbolic manifolds},
journal = {Complex Manifolds},
volume = {3},
year = {2016},
zbl = {1342.32016},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_coma-2016-0006}
}
Roberto Mossa. Diastatic entropy and rigidity of complex hyperbolic manifolds. Complex Manifolds, Tome 3 (2016) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_coma-2016-0006/