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Eigenvalue Estimates of the spincDirac Operator and Harmonic Forms on Kähler-Einstein Manifolds
- Source :
- Symmetry, Integrability and Geometry: Methods and Applications.
- Publication Year :
- 2015
- Publisher :
- SIGMA (Symmetry, Integrability and Geometry: Methods and Application), 2015.
-
Abstract
- We establish a lower bound for the eigenvalues of the Dirac operator defined on a compact K\"ahler-Einstein manifold of positive scalar curvature and endowed with particular ${\rm spin}^c$ structures. The limiting case is characterized by the existence of K\"ahlerian Killing ${\rm spin}^c$ spinors in a certain subbundle of the spinor bundle. Moreover, we show that the Clifford multiplication between an effective harmonic form and a K\"ahlerian Killing ${\rm spin}^c$ spinor field vanishes. This extends to the ${\rm spin}^c$ case the result of A. Moroianu stating that, on a compact K\"ahler-Einstein manifold of complex dimension $4\ell+3$ carrying a complex contact structure, the Clifford multiplication between an effective harmonic form and a K\"ahlerian Killing spinor is zero.
- Subjects :
- Mathematics - Differential Geometry
Condensed Matter::Quantum Gases
Spinor
Einstein manifold
Spinor bundle
Clifford analysis
Dirac operator
53C27, 53C25, 53C55, 58J50, 83C60
General Relativity and Quantum Cosmology
symbols.namesake
Spinor field
Killing spinor
Quantum mechanics
symbols
Mathematics::Differential Geometry
Geometry and Topology
Mathematics::Symplectic Geometry
Mathematical Physics
Analysis
Mathematics
Mathematical physics
Scalar curvature
Subjects
Details
- ISSN :
- 18150659
- Database :
- OpenAIRE
- Journal :
- Symmetry, Integrability and Geometry: Methods and Applications
- Accession number :
- edsair.doi.dedup.....754d3fee08f2c6f795da5a92ce090c54