2007/07/02 by Georges Habib
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Dirac operator #Exact solutions in general relativity #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Holonomy #Manifold (fluid mechanics) #Mathematical analysis #Mathematical physics #Mathematics #Physics #Pseudo-Riemannian manifold #Pullback #Pure mathematics #Ricci curvature #Riemann curvature tensor #Spin (aerodynamics) #Spinor #Tensor (intrinsic definition) #Tensor density #Tensor field #Weyl tensor #math.DG
paper · pdf · doi:10.1016/j.geomphys.2007.07.002
arxiv created 2007/07/02 · openalex publication_date 2007/07/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this paper, we give a new lower bound for the eigenvalues of the Dirac operator on a compact spin manifold. This estimate is motivated by the fact that in its limiting case a skew-symmetric tensor (see Equation \eqrefeq:16) appears that can be identified geometrically with the O'Neill tensor of a Riemannian flow, carrying a transversal parallel spinor. The Heisenberg group which is a fibration over the torus is an example of this case. Sasakian manifolds are also considered as particular examples of Riemannian flows. Finally, we characterize the 3-dimensional case by a solution of the Dirac equation