Abstract
We study the first positive eigenvalue λ(p)1 of the Laplacian on p-forms for oriented closed Riemannian manifolds. It is known that the inequality λ(1)1≤λ(0)1 holds in general. In the present paper, a Riemannian manifold is said to have the gap if the strict inequality λ(1)1<λ(0)1 holds. We show that any oriented closed manifold M with the first Betti number b1(M)=0 whose dimension is bigger than two, admits two Riemannian metrics, the one with the gap and the other without the gap.
Original language | English |
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Pages (from-to) | 307-320 |
Number of pages | 14 |
Journal | Journal of the Mathematical Society of Japan |
Volume | 53 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2001 |
Externally published | Yes |
Keywords
- Eigenvalue
- Einstein manifold
- Laplacian on forms
- Stability
ASJC Scopus subject areas
- Mathematics(all)