Characterizing S m by the Spectrum of the Laplacian on 2-Forms

S. I. Goldberg, H. Gauchman
1987 Proceedings of the American Mathematical Society  
The Euclidean sphere S2n+1 is characterized by the spectrum of the Laplacian on 2-forms in all dimensions. 2. The spectrum. Let (M, g) be a compact connected C°° Riemannian manifold without boundary, and with Laplacian A = -{dd* + d*d), where d is the operator of exterior differentiation and d* is its adjoint with respect to the Riemannian metric g. Then, for each p = 0,1,2,.
doi:10.2307/2046487 fatcat:4ar5iixamjbgfa7ksm7asq3s2a