Loop Spaces as Hilbert-Hartogs Manifolds

TL;DR

This paper demonstrates that generalized loop spaces of Hartogs manifolds are Hilbert-Hartogs and explores their extension properties, providing examples and enhancing understanding of their structure in complex analysis.

Contribution

It establishes that loop spaces of Hartogs manifolds are Hilbert-Hartogs and improves the understanding of their extension properties with new examples.

Findings

Loop spaces of Hartogs manifolds are Hilbert-Hartogs.

Hilbert-Hartogs manifolds have better extension properties.

Provided examples of Hilbert-Hartogs manifolds.

Abstract

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.