Complete nonsingular holomorphic foliations on Stein manifolds Alarcón López, Antonio Forstnerič, Franc Stein manifold Complete holomorphic foliation Density property Alarcón is partially supported by the State Research Agency (AEI) via the grant no. PID2020-117868GB-I00 and the “Maria de Maeztu” Excellence Unit IMAG, reference CEX2020-001105-M, funded by MCIN/AEI/10.13039/501100011033/, Spain. Forstneric is supported by the European Union (ERC Advanced grant HPDR, 101053085) and grants P1-0291, J1-3005, and N1-0237 from ARRS, Republic of Slovenia. We thank an anonymous referee for useful remarks, and the editor for the suggestion to make the introduction more accessible to a wider audience. Funding for open access publishing: Universidad de Granada/CBUA. 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. 2024-01-08T12:18:36Z 2024-01-08T12:18:36Z 2024-01-03 info:eu-repo/semantics/article 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] https://hdl.handle.net/10481/86616 10.1007/s00009-023-02566-0 eng http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess Attribution-NonCommercial-NoDerivatives 4.0 Internacional Springer Nature