Estimates of small Dirac eigenvalues on 3-dimensional Sasakian manifolds
| Autor: | Eui Chul Kim |
|---|---|
| Rok vydání: | 2010 |
| Předmět: |
Dirac operator
Dirac (software) Spectrum (functional analysis) Mathematical analysis Zero (complex analysis) Eigenvalues Manifold Sasakian manifold symbols.namesake Computational Theory and Mathematics symbols Geometry and Topology Analysis Eigenvalues and eigenvectors Scalar curvature Mathematical physics Mathematics |
| Zdroj: | Differential Geometry and its Applications. 28:648-655 |
| ISSN: | 0926-2245 |
| Popis: | On a 3-dimensional closed Sasakian spin manifold ( M 3 , g ) , the spectrum of the Dirac operator D is in general not symmetric with respect to zero. Let λ 1 − 0 and λ 1 + > 0 be the first negative and positive eigenvalue of D , respectively. Let S min denote the minimum of the scalar curvature of ( M 3 , g ) with S min > − 3 2 . We prove in this paper that λ 1 − ⩽ 1 − 2 S min + 4 2 holds generally and that λ 1 + satisfies λ 1 + ⩾ S min + 6 8 whenever λ 1 + belongs to the interval λ 1 + ∈ ( 1 2 , 5 2 ) . It turns out that each of these estimates improves Friedrich's inequality for the first eigenvalue of the Dirac operator [Th. Friedrich, Der erste Eigenwert des Dirac-Operators einer kompakten Riemannschen Mannigfaltigkeit nichtnegativer Skalarkrummung, Math. Nachr. 97 (1980) 117–146]. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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