Abstract:
:Let X = Omega/Gamma be a compact quotient of an irreducible bounded symmetric domain Omega of rank >/=2 by a discrete group omega of automorphisms without fixed points. It is well known that the Kähler-Einstein metric g on X carries seminegative curvature (in the sense of Griffiths). I show that any Hermitian metric h on X carrying seminegative curvature must be a constant multiple of g. This can be applied to prove rigidity theorems of holomorphic maps from X into Hermitian manifolds (Y, k) carrying seminegative curvature. These results are also generalized to the case of quotients of finite volume. On the other hand, let (X(c), g(c)) be an irreducible compact Hermitian symmetric manifold of rank >/=2. Then g(c) is Kähler and carries semipositive holomorphic bisectional curvature. I prove that any Kähler h on X(c) carrying semipositive holomorphic bisectional curvature must be equal to g(c) up to a constant multiple and up to a biholomorphic transformation of X(c).
journal_name
Proc Natl Acad Sci U S Aauthors
Mok Ndoi
10.1073/pnas.83.8.2288subject
Has Abstractpub_date
1986-04-01 00:00:00pages
2288-90issue
8eissn
0027-8424issn
1091-6490journal_volume
83pub_type
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