Complete nonsingular holomorphic foliations on Stein manifolds
Metadatos
Mostrar el registro completo del ítemEditorial
Springer Nature
Materia
Stein manifold Complete holomorphic foliation Density property
Fecha
2024-01-03Referencia bibliográfica
Antonio Alarcón and Franc Forstnerič, Complete nonsingular holomorphic foliations on Stein manifolds. Mediterr. J. Math. 21, 25 (2024). [https://doi.org/10.1007/s00009-023-02566-0]
Patrocinador
MCIN/AEI/10.13039/ 501100011033/, Spain: PID2020-117868GB-I00; MCIN/AEI/10.13039/ 501100011033/, Spain: “Maria de Maeztu” Excellence Unit IMAG, CEX2020-001105-M; European Union: ERC Advanced HPDR, 101053085; ARRS, Republic of Slovenia: P1-0291, J1-3005, N1- 0237; Universidad de Granada/CBUAResumen
Let X be a Stein manifold of complex dimension n > 1 endowed with a Riemannian metric g. We show that for every integer k
with [ n
2
] ≤ k ≤ n − 1 there is a nonsingular holomorphic foliation of
dimension k on X all of whose leaves are closed and g-complete. The
same is true if 1 ≤ k < [ n
2
] provided that there is a complex vector
bundle epimorphism T X → X × Cn−k . We also show that if F is a
proper holomorphic foliation on Cn (n > 1) then for any Riemannian
metric g on Cn there is a holomorphic automorphism Φ of Cn such that
the image foliation Φ∗F is g-complete. The analogous result is obtained
on every Stein manifold with Varolin’s density property.