arXiv subjects
Publications and source records attributed to M. Anakkar.
We prove that the loop space of a K\"ahler manifold inherits a K\"ahler structure. Then we prove that equipped with this natural metric the loop space is complete and unbounded. Additionally, we show that a geodesic on the loop space can be constructed by piecing together geodesics from each individual leaf.
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 postulated in their definition. Finally, we give a list of examples of Hilbert-Hartogs manifolds.
We prove some extension results for holomorphic mappings with values in complex Hilbert manifolds