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

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

1999-06-25

arxiv.org/abs/math/9906168v1

Mathematics

Differential Geometry

Latex2.09, 14 pages

Scientific paper

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.

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