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math.DG2002
A relation between the Ricci tensor and the spectrum of the Dirac operator
Klaus-Dieter Kirchberg
Using Weitzenböck techniques on any compact Riemannian spin manifold we derive a general inequality depending on a real parameter and joining the spectrum of the Dirac operator wit…
math.DG2001
Eigenvalue estimates of the Dirac operator depending on the Ricci tensor
Thomas Friedrich, Klaus-Dieter Kirchberg
We prove a new lower bound for the first eigenvalue of the Dirac operator on a compact Riemannian spin manifold by refined Weitzenböck techniques. It applies to manifolds with harm…
math.DG1998
Holomorphic spinors and the Dirac equation
Klaus-Dieter Kirchberg
A closed spin Kähler manifold of positive scalar curvature with smallest possible first eigenvalue of the Dirac operator is characterized by holomorphic spinors. It is shown that o…