The transversal wave equation and the noncommutative geodesic flow in Riemannian foliations

1997/03/21 by Yuri A. Kordyukov, Kordyukov, Yuri A.
Mathematics · #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #dg-ga #math.DG

paper · pdf · doi:10.48550/arxiv.dg-ga/9703015

LaTeX 2.09, 19 pages

arxiv created 1997/03/21 · openalex publication_date 1997/03/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the transversal wave equation on a compact Riemannian foliated manifold. As applications, we get an Egorov's type theorem for transversally elliptic operators, state a relationship between the singularities of the Fourier transform of the spectrum distribution function of a transversally elliptic operator and the corresponding transversal bicharacteristic flow and give a description of the noncommutative geodesic flow in transversal geometry of Riemannian foliations.

Related

• On transversally harmonic maps of foliated Riemannian manifolds
• Noncommutative spectral geometry of Riemannian foliations: some results and open problems
• Dynamic First Order Wave Systems with Drift Term on Riemannian Manifolds
• Geometric Wave Equations
• The trace formula for transversally elliptic operators on Riemannian foliations