ON EIGENVALUE ESTIMATES FOR THE SUBMANIFOLD DIRAC OPERATOR

DOI10.1142/S0129167X0200140XzbMath1049.58028arXivmath/0103095OpenAlexW2029668859MaRDI QIDQ4807410

Bertrand Morel, Nicolas Ginoux

Publication date: 18 May 2003

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0103095

zbMATH Keywords

spectrumDirac operatorsubmanifoldsconformal geometrycoDirac operator

Mathematics Subject Classification ID

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

Related Items (13)

The twisted \(\mathrm{Spin}^c\) Dirac operator on Kähler submanifolds of the complex projective space ⋮ Complex and Lagrangian surfaces of the complex projective plane via Kählerian Killing \(\mathrm{Spin}^c\) spinors ⋮ Extrinsic conformal lower bounds of eigenvalue for Dirac operator ⋮ Lower bounds for the eigenvalue estimates of the submanifold Dirac operator ⋮ The Dirac-Witten operator on pseudo-Riemannian manifolds ⋮ Spinorial representation of surfaces into 4-dimensional space forms ⋮ Some remarks on the Dirac-Witten operator on pseudo-Riemannian manifolds ⋮ The spectrum of the twisted Dirac operator on Kähler submanifolds of the complex projective space ⋮ Twisted Dirac operator on minimal submanifolds ⋮ Generalized Weierstrass relations and Frobenius reciprocity ⋮ Dirac operators on Lagrangian submanifolds ⋮ Lower bounds for the eigenvalues of the \(\mathrm{Spin}^c\) Dirac operator on submanifolds ⋮ Estimation on the Spin${}^c$ twisted Dirac operators

Cites Work

• A conformal lower bound for the smallest eigenvalue of the Dirac operator and Killing spinors
• Lower bounds for eigenvalues of hypersurface Dirac operators
• Extrinsic bounds for eigenvalues of the Dirac operator
• A remark on: Lower bounds for eigenvalues of hypersurface Dirac operators
• A new proof of the positive energy theorem.
• The Einstein-Dirac equation on Riemannian spin manifolds
• Real Killing spinors and holonomy
• Der erste Eigenwert des Dirac‐Operators einer kompakten, Riemannschen Mannigfaltigkeit nichtnegativer Skalarkrümmung
• Eigenvalue estimates for the Dirac-Schröder operators
• Dirac operator on embedded hypersurfaces

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