On the diastatic entropy and C^1-rigidity of complex hyperbolic manifolds

Mossa R.

2019-01-01

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Abstract

Let f:(Y,g)→(X,g 0 ) be a nonzero degree continuous map between compact Kähler manifolds of dimension n≥2, where g 0 has constant negative holomorphic sectional curvature. Adapting the Besson–Courtois–Gallot barycentre map techniques to the Kähler 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].