Tohoku Mathematical Journal
- Tohoku Math. J. (2)
- Volume 52, Number 2 (2000), 261-270.
The first eigenvalues of finite Riemannian covers
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.
Tohoku Math. J. (2), Volume 52, Number 2 (2000), 261-270.
First available in Project Euclid: 3 May 2007
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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