The Hijazi inequality on conformally parabolic manifolds
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Submission date: 02. Jun. 2008
published in: Differential geometry and its applications, 29 (2011) 6, p. 838-849
DOI number (of the published article): 10.1016/j.difgeo.2011.08.011
MSC-Numbers: 53C27, 53C21
Keywords and phrases: dirac operator, conformally parabolic manifold, conformal geometry
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We prove the Hijazi inequality, an estimate for Dirac eigenvalues, for complete manifolds of finite volume. Under some additional assumptions on the dimension and the scalar curvature, this inequality is also valid for elements of the essential spectrum. This allows to prove the conformal version of the Hijazi inequality on conformally parabolic manifolds if the spin analog to the Yamabe invariant is positive.