Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 18 (2022), 091, 16 pages      arXiv:2009.03276      https://doi.org/10.3842/SIGMA.2022.091

Ray-Singer Torsion and the Rumin Laplacian on Lens Spaces

Akira Kitaoka
Graduate School of Mathematical Sciences, The University of Tokyo, Japan

Received May 19, 2022, in final form November 14, 2022; Published online November 28, 2022

Abstract
We express explicitly the analytic torsion functions associated with the Rumin complex on lens spaces in terms of the Hurwitz zeta function. In particular, we find that the functions vanish at the origin and determine the analytic torsions. Moreover, we have a formula between this torsion and the Ray-Singer torsion.

Key words: analytic torsion; Rumin complex; CR geometry; contact geometry.

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