Spectra of Unit Tangent Bundles of Compact Hyperbolic Riemann Surfaces

Abstract:

Recent results of Gordon, Mao and Pesce imply that isospectral compact hyperbolic Riemann surfaces have Laplace and length isospectral unit tangent bundles. In this note we give explicit formulae relating the spectra of such surfaces and those of their unit tangent bundles, and use them to prove the converses.

Keywords: Laplace spectrum; length spectrum; Riemann surfaces; Sasaki metric

Language: English

Document Type: Regular paper

Affiliations: 1: FaMAF, Ciudad Universitaria, 5000 Córdoba, Argentina (E-mail: salvai@mate.uncor.edu)