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

研究成果: Article査読

5 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 < 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.

本文言語English
ページ(範囲)306-319
ページ数14
ジャーナルJournal of the Mathematical Society of Japan
53
2
出版ステータスPublished - 2001 4月 1
外部発表はい

ASJC Scopus subject areas

  • 数学 (全般)

フィンガープリント

「On the gap between the first eigenvalues of the Laplacian on functions and 1-forms」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル