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題 名 | Riemannian DNA, Inequalities and Their Applications |
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作 者 | Chen,Bang-yen; | 書刊名 | 淡江理工學刊 |
卷 期 | 3:3 2000.11[民89.11] |
頁 次 | 頁123-130 |
分類號 | 316.1 |
關鍵詞 | 黎曼不等式; 平方平均曲率; 張力; Riemannian invariants; Squared mean curvature; Tension; Ideal immersion; Best way of living; Riemannian DNA; |
語 文 | 英文(English) |
英文摘要 | The main purpose of this survey article is to present the new type of Riemannian curvature invariants (Riemannian DNA) and the sharp inequalities, involving these invariants and the squared mean curvature, originally introduced and established in [7,8]. These Riemannia DNA affect the behavior in general of the Riemannian manifold and they have several interesting connections to several areas of mathematics. For instance, they give rise to new obstructions to minimal and Lagrangian isometric immersions. Moreover, these invariants relate closely to the first nonzero eigenvalue of the Laplacian on a Riemannian manifold. These invariants together with the sharp inequalities gives rise naturally to the notion of “ideal immersions” or the notion of “the best ways of living”. We also explain the physical meaning of the notion of ideal immersions for Riemannian manifolds in a Riemannian space form based again on the sharp inequalities. |
本系統中英文摘要資訊取自各篇刊載內容。