Eigenvalue estimates for Dirac operators with parallel characteristic torsion
| Autor: | Mario Kassuba, Ilka Agricola, Thomas Friedrich |
|---|---|
| Rok vydání: | 2008 |
| Předmět: |
Mathematics - Differential Geometry
Pure mathematics Momentum operator Dirac operator Eigenvalue estimate FOS: Physical sciences Deformed spin connection Semi-elliptic operator symbols.namesake Dolbeault operator FOS: Mathematics Mathematics::Symplectic Geometry Mathematical Physics Mathematics Skew-symmetric torsion Position operator Mathematical analysis Mathematical Physics (math-ph) Clifford analysis Compact operator Cubic Dirac operator 53C25 81T30 Ladder operator Differential Geometry (math.DG) Computational Theory and Mathematics Spectral asymmetry symbols Characteristic connection Mathematics::Differential Geometry Geometry and Topology Analysis |
| Zdroj: | Differential Geometry and its Applications. 26:613-624 |
| ISSN: | 0926-2245 |
| DOI: | 10.1016/j.difgeo.2008.04.010 |
| Popis: | Assume that the compact Riemannian spin manifold $(M^n,g)$ admits a $G$-structure with characteristic connection $\nabla$ and parallel characteristic torsion ($\nabla T=0$), and consider the Dirac operator $D^{1/3}$ corresponding to the torsion $T/3$. This operator plays an eminent role in the investigation of such manifolds and includes as special cases Kostant's ``cubic Dirac operator'' and the Dolbeault operator. In this article, we describe a general method of computation for lower bounds of the eigenvalues of $D^{1/3}$ by a clever deformation of the spinorial connection. In order to get explicit bounds, each geometric structure needs to be investigated separately; we do this in full generality in dimension 4 and for Sasaki manifolds in dimension 5. Comment: 16 pages, 4 figures |
| Databáze: | OpenAIRE |
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