Some remarks on the Hijazi inequality and generalizations of the Killing equation for spinors

DOI10.1016/S0393-0440(99)00049-2zbMath0979.53052arXivmath/9906168MaRDI QIDQ5927603

Thomas Friedrich, Eui Chul Kim

Publication date: 17 February 2002

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9906168

zbMATH Keywords

eigenvalueDirac operatorKilling equationscalar curvaturespinors and twistors

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Spin and Spin({}^c) geometry (53C27)

Related Items (22)

Remark on the limit case of positive mass theorem for manifolds with inner boundary ⋮ Cauchy spinors on 3-manifolds ⋮ THE ENERGY-MOMENTUM TENSOR ON LOW DIMENSIONAL Spin^c MANIFOLDS ⋮ Spinors of real type as polyforms and the generalized Killing equation ⋮ Spinors in 2022 ⋮ Generalized Killing spinors on spheres ⋮ Spinorial description of \(\mathrm{SU}(3)\)- and \(\mathrm{G}_2\)-manifolds ⋮ Limiting case of the spin hypersurface Dirac operator arising in the positive mass theorem for black holes ⋮ Generalization of Kim's estimates in terms of the trace of divergence‐free symmetric tensor ⋮ An estimate on the nodal set of eigenspinors on closed surfaces ⋮ Generalized Killing spinors and Lagrangian graphs ⋮ THE ENERGY-MOMENTUM TENSOR ON Spin^c MANIFOLDS ⋮ \(\mathcal{N}=1\) geometric supergravity and chiral triples on Riemann surfaces ⋮ Generalized Killing spinors on Einstein manifolds ⋮ Eigenvalue estimates for the Dirac-Schröder operators ⋮ Generalized cylinders in semi-Riemannian and spin geometry ⋮ Eigenvalue estimates via weighted \(L^2\)-technique ⋮ \(\sigma_k\)-scalar curvature and eigenvalues of the Dirac operator ⋮ Some estimates over spacelike spin hypersurfaces of Lorentzian manifold ⋮ REDUCED HOLONOMY, HYPERSURFACES AND EXTENSIONS ⋮ Geometric and analytic properties of families of hypersurfaces in Eguchi--Hanson space ⋮ Estimation on the Spin${}^c$ twisted Dirac operators

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Spin manifolds, Killing spinors and universality of the Hijazi inequality
• Lower eigenvalue estimates for Dirac operators
• A conformal lower bound for the smallest eigenvalue of the Dirac operator and Killing spinors
• Eigenvalue bounds for the Dirac operator
• On the spinor representation of surfaces in Euclidean \(3\)-space
• Lower bounds for the eigenvalues of the Dirac operator
• A comparison of the eigenvalues of the Dirac and Laplace operators on a two-dimensional torus
• The Yamabe problem
• Der erste Eigenwert des Dirac‐Operators einer kompakten, Riemannschen Mannigfaltigkeit nichtnegativer Skalarkrümmung

This page was built for publication: Some remarks on the Hijazi inequality and generalizations of the Killing equation for spinors