On properly essential classical conformal diffeomorphism groups

2011/07/29 by Stefan Müller, Müller, Stefan, Peter Spaeth +1
Mathematics · #53A30 #53D35 #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Symplectic Geometry (math.SG) #math.SG #msc:53A30 #msc:53D35

paper · pdf · doi:10.48550/arxiv.1107.5861

13 pages

arxiv created 2011/07/29 · openalex publication_date 2011/07/29 · arxiv updated 2011/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that various classical conformal diffeomorphism groups, which are known to be essential [1], are in fact properly essential. This is a consequence of a local criterion on a conformal diffeomorphism in the form of a cohomological equation. Furthermore, we study the orbit of a tensor field under the action of the conformal diffeomorphism group for these classical conformal structures. On every closed contact manifold, we find conformal contact forms that are not diffeomorphic.

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