Diastatic entropy and rigidity of complex hyperbolic manifolds

• Autorzy: Roberto Mossa
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: De Gruyter Open
• Czasopismo: Complex Manifolds
• Rocznik: 2016
• Tom: 3
• Numer: 1

Daty

otrzymano

2016-03-12

zaakceptowano

2016-05-01

online

2016-05-13

Twórcy

autor

Roberto Mossa

• Departamento de Matemática, Universidade Federal de Santa Catarina, Campus Universitário Trindade, CEP 88.040-900, Florianópolis, SC, Brasil

Identyfikatory

DOI

10.1515/coma-2016-0006