Energy–momentum tensor on foliations

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• 作者：Georges Habib
• 关键词：Dirac operator ; Energy&#x2013 ; momentum tensor ; Hypersurfaces ; Second fundamental form ; Riemannian flows ; O&#x2019 ; Neill tensor
• 刊名：Journal of Geometry and Physics
• 出版年：2007
• 期刊代码：29_03930440
• 类别：ph
• 出版时间：October 2007
• 卷：57
• 期：11
• 页码：2234-2248
• 文件大小：324 K

摘要

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 Eq. (1.6)) 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 to be particular examples of Riemannian flows. Finally, we characterize the 3-dimensional case by a solution of the Dirac equation.