On the gap between the first eigenvalues of the laplacian on functions and 1-forms

研究成果: ジャーナルへの寄稿学術論文査読

1 被引用数 (Scopus)

抄録

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(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.

本文言語英語
ページ(範囲)307-320
ページ数14
ジャーナルJournal of the Mathematical Society of Japan
53
2
DOI
出版ステータス出版済み - 2001

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