Some Remarks on the Hijazi Inequality and Generalizations of the Killing Equation for Spinors

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We generalize the well-known lower estimates for the first eigenvalue of the Dirac operator on a compact Riemannian spin manifold proved by Th. Friedrich (1980) and O. Hijazi (1986, 1992). The special solutions of the Einstein-Dirac equation constructed recently by Friedrich/Kim are examples for the limiting case of these inequalities. The discussion of the limiting case of these estimates yields two new field equations generalizing the Killing equation as well as the weak Killing equation for spinor fields. Finally, we discuss the 2- and 3-dimensional case in more detail.
Latex2.09, 14 pages

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Differential Geometry, 53C25, 58G30

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http://salesiana.dossiersoluciones.com/handle/123456789/78718

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9906168
 http://arxiv.org/abs/math/9906168

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arXiv