An upper bound for the first eigenvalue of the Dirac operator on compact spin manifolds

DOI10.1007/BF02571352zbMath0722.53036OpenAlexW2081761147MaRDI QIDQ756160

Helga Baum

Publication date: 1991

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/174234

zbMATH Keywords

upper boundsDirac operatorsectional curvaturespin manifoldinjectivity radiusfirst eigenvalue

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Elliptic equations on manifolds, general theory (58J05) Global Riemannian geometry, including pinching (53C20)

Related Items (12)

Vafa-Witten estimates for compact symmetric spaces ⋮ The evolution of the Dirac field in curved space-times ⋮ A spinorial characterization of hyperspheres ⋮ An estimate on the nodal set of eigenspinors on closed surfaces ⋮ Upper bounds of small eigenvalues of the Dirac operator and isometric immersions ⋮ Lower bounds for eigenvalues of the Dirac operator on \(n\)-spheres with \(SO(n)\)-symmetry ⋮ Noncommutative geometry and conformal geometry. III: Vafa-Witten inequality and Poincaré duality ⋮ Inequalities of eigenvalues for the Dirac operator on compact complex spin submanifolds in complex projective spaces ⋮ Vafa-Witten bound on the complex projective space ⋮ Lower bounds for eigenvalues of the Dirac operator on surfaces of rotation ⋮ Extrinsic estimates for eigenvalues of the Dirac operator ⋮ Upper bounds for the first eigenvalue of the Dirac operator on surfaces

Cites Work

• Complete Riemannian manifolds with imaginary Killing spinors
• Harmonic spinors
• Der erste Eigenwert des Dirac‐Operators einer kompakten, Riemannschen Mannigfaltigkeit nichtnegativer Skalarkrümmung
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