3 papers
math.DG2025
Loop space of a Kähler manifold
M. Anakkar
We prove that the loop space of a Kähler manifold inherits a Kähler structure. Then we prove that equipped with this natural metric the loop space is complete and unbounded. Additi…
math.CV2024
Non-existence of a holomorphic embedding of the Sobolev loop space into the projective Hilbert space
Anakkar M., S. Ivashkovich
The goal of this paper is to understand the properties of meromorphic mappings with values in two model complex Hibert manifolds: projective Hilbert space $\pp(l^2)$ and Sobolev lo…
math.CV2019
Loop Spaces as Hilbert-Hartogs Manifolds
M. Anakkar, S. Ivashkovich
We prove that generalized loop spaces of Hartogs manifolds are Hilbert-Hartogs. We prove also that Hilbert-Hartogs manifolds possess a better extension properties that it is postul…