Spin manifolds,killing spinors and universality of the Hijazi inequality |
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Authors: | André Lichnerowicz |
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Institution: | (1) Collège de France, 11 Place Marcelin Berthelot, F-75231 Paris Cédex 05, France |
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Abstract: | In terms of the Dirac operator P, we introduce on any field a first-order operator D and show that the operator ( – ) on the spinors ( =(n/4(n–1))R; dim W=n) is positive. By means of a universal formula, we show that, on a compact spin manifold of dimension 3, the Hijazi inequality 8] holds for every spinor field such that (P , P ) =
2( , ) ( =const.). In the limiting case, the manifold admits a Killing spinor which can be evaluated in terms of . Different properties of spin manifolds admitting Killing spinors are proved. D is nothing but the twistor operator . |
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Keywords: | |
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