Let M be a Kobayashi hyperbolic homogeneous manifold. Let F be a holomorphic foliation on M invariant under a transitive group G of bi-holomorphisms. We prove that the leaves of F are the fibers of a holomorphic G-equivariant submersion pi : M -> N onto a G-homogeneous complex manifold N. We also show that if Q is an automorphism family of a hyperbolic convex (possibly unbounded) domain D in C-n, then the fixed point set of Q is either empty or a connected complex submanifold of D.
Bracci, F., Iannuzzi, A., Mckay, B. (2016). Invariant holomorphic foliations on kobayashi hyperbolic homogeneous manifolds. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 144(4), 1619-1629 [10.1090/proc/12817].
Invariant holomorphic foliations on kobayashi hyperbolic homogeneous manifolds
Bracci F.
;Iannuzzi A.;
2016-01-01
Abstract
Let M be a Kobayashi hyperbolic homogeneous manifold. Let F be a holomorphic foliation on M invariant under a transitive group G of bi-holomorphisms. We prove that the leaves of F are the fibers of a holomorphic G-equivariant submersion pi : M -> N onto a G-homogeneous complex manifold N. We also show that if Q is an automorphism family of a hyperbolic convex (possibly unbounded) domain D in C-n, then the fixed point set of Q is either empty or a connected complex submanifold of D.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
