On the diastatic entropy and C^1-rigidity of complex hyperbolic manifolds
Differential Geometry
2019-05-06 v1
Abstract
Let f:(Y,g)->(X,g_0) be a non zero degree continuous map between compact K\"ahler manifolds of dimension greater or equal to 2, where g_0 has constant negative holomorphic sectional curvature. Adapting the Besson-Courtois-Gallot barycentre map techniques to the K\"ahler setting, we prove a gap theorem in terms of the degree of f and the diastatic entropies of (Y, g) and (X,g_0), which extends the rigidity result proved by the author in [13].
Keywords
Cite
@article{arxiv.1905.01284,
title = {On the diastatic entropy and C^1-rigidity of complex hyperbolic manifolds},
author = {Roberto Mossa},
journal= {arXiv preprint arXiv:1905.01284},
year = {2019}
}
Comments
23 pages