Microlocal Analysis of Some Isospectral Deformations

Abstract

We study the microlocal structure of the examples of isospectral deformations of Riemannian manifolds given by D. DeTurck and C. Gordon in [DeT-G1]. The Schwartz kernel of the intertwining operators considered by them may be written as an oscillatory integral with a singular phase function and product type amplitude. In certain instances, we identify them as belonging to the space of Fourier integral operators associated with various pairwise intersecting Lagrangians. After formulating a class of operators incorporating the most relevant features of the operators above, we establish a composition calculus for this class and show that is not necessary to introduce new Lagrangians in the composition.