Tohoku Mathematical Journal

The first eigenvalues of finite Riemannian covers

Katsuhiro Yoshiji

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Abstract

There exists a Riemannian metric on the real projective space such that the first eigenvalue coincides with that of its Riemannian universal cover, if the dimension is bigger than 2. For the proof, we deform the canonical metric on the real projective space. A similar result is obtained for lens spaces, as well as for closed Riemannian manifolds with Riemannian double covers. As a result, on a non-orientable closed manifold other than the real projective plane, there exists a Riemannian metric such that the first eigenvalue coincides with that of its Riemannian double cover.

Article information

Source
Tohoku Math. J. (2), Volume 52, Number 2 (2000), 261-270.

Dates
First available in Project Euclid: 3 May 2007

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1178224610

Digital Object Identifier
doi:10.2748/tmj/1178224610

Mathematical Reviews number (MathSciNet)
MR1756097

Zentralblatt MATH identifier
0965.58026

Subjects
Primary: 58J50: Spectral problems; spectral geometry; scattering theory [See also 35Pxx]

Citation

Yoshiji, Katsuhiro. The first eigenvalues of finite Riemannian covers. Tohoku Math. J. (2) 52 (2000), no. 2, 261--270. doi:10.2748/tmj/1178224610. https://projecteuclid.org/euclid.tmj/1178224610


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