Energy–momentum tensor on foliations |
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Authors: | Georges Habib |
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Institution: | Institut Élie Cartan, Université Henri Poincaré, Nancy I, B.P. 239 54506 Vandœuvre-Lès-Nancy Cedex, France |
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Abstract: | 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. |
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Keywords: | 53C27 53C12 53C25 57C30 |
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