GEODESIC-EINSTEIN METRICS AND NONLINEAR STABILITIES
Artikel i vetenskaplig tidskrift, 2019

In this paper, we introduce notions of nonlinear stabilities for a relative ample line bundle over a holomorphic fibration and define the notion of a geodesic-Einstein metric on this line bundle, which generalize the classical stabilities and Hermitian-Einstein metrics of holomorphic vector bundles. We introduce a Donaldson type functional and show that this functional attains its absolute minimum at geodesic-Einstein metrics, and we also discuss the relations between the existence of geodesic-Einstein metrics and the nonlinear stabilities of the line bundle. As an application, we will prove that a holomorphic vector bundle admits a Finsler-Einstein metric if and only if it admits a Hermitian-Einstein metric, which answers a problem posed by S. Kobayashi.

Författare

Huitao Feng

Nankai University

Kefeng Liu

University of California at Los Angeles

Capital Normal University

Xueyuan Wan

Chalmers, Matematiska vetenskaper, Algebra och geometri

Transactions of the American Mathematical Society

0002-9947 (ISSN) 1088-6850 (eISSN)

Vol. 371 11 8029-8049

Ämneskategorier

Algebra och logik

Geometri

Matematisk analys

DOI

10.1090/tran/7658

Mer information

Senast uppdaterat

2019-08-19