The Hijazi inequality on conformally parabolic manifolds

作者：Grosse Nadine^*

来源：Differential Geometry and its Applications, 2011, 29(6): 838-849.

DOI：10.1016/j.difgeo.2011.08.011

• Dirac operator
• Conformally parabolic manifold
• Conformal geometry

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.

• 出版日期2011-12