9 citations · 24 across the 8 of their papers we have counts for
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Eigenvalue Estimates For The Dirac Operator On Kaehler-Einstein Manifolds Of Even Complex Dimension
K. -D. Kirchberg
In Kähler-Einstein case of positive scalar curvature and even complex dimension, an improved lower bound for the first eigenvalue of the Dirac operator is given. It is shown by a g…
Integrability Conditions For Almost Hermitian And Almost Kaehler 4-Manifolds
Klaus-Dieter Kirchberg
If denotes the self dual part of the Weyl tensor of any Kähler 4-manifold and its scalar curvature, then the relation is well-known. For any almost Kähl…
Curvature dependent lower bounds for the first eigenvalue of the Dirac operator
K. -D. Kirchberg
Using Weitzenböck techniques on any compact Riemannian spin manifold we derive inequalities that involve a real parameter and join the eigenvalues of the Dirac operator with curvat…
Some integrability conditions for almost Kähler manifolds
Klaus-Dieter Kirchberg
Among other results, a compact almost Kähler manifold is proved to be Kähler if the Ricci tensor is semi-negative and its length coincides with that of the star Ricci tensor or if…
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…
Eigenvalue estimates for the Dirac operator depending on the Weyl curvature tensor
Thomas Friedrich, Klaus-Dieter Kirchberg
We prove new lower bounds for the first eigenvalue of the Dirac operator on compact manifolds whose Weyl tensor or curvature tensor, respectively, is divergence free. In the specia…
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…
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…