New spectral characterization theorems for S²

Martin Engman

Vol. 154 (1992), No. 2, 215–229

DOI: 10.2140/pjm.1992.154.215

Abstract

Two theorems are proved: (1) Among surfaces of revolution which are diffeomorphic to S², the constant curvature metric is completely characterized by the multiplicities of its eigenvalues and, (2) If the square of an eigenfunction is, again, an eigenfunction then the metric is the standard metric on S².

Mathematical Subject Classification

Primary: 58G25

Milestones

Received: 14 March 1991

Published: 1 June 1992