arXiv subjects

K. -D. Kirchberg

Publications and source records attributed to K. -D. Kirchberg.

2 recordsLinked to original sources

arXiv2009

Eigenvalue Estimates For The Dirac Operator On Kaehler-Einstein Manifolds Of Even Complex Dimension

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 general construction that there are manifolds for which this new lower bound itself is the first eigenvalue.

math.DG↗

arXiv2003

Curvature dependent lower bounds for the first eigenvalue of the Dirac operator

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 curvature terms. The discussion of these inequalities yields vanishing theorems for the kernel of the Dirac operator $D$ and lower bounds for the spectrum of $D^2$ if the curvature satisfies certain conditions.

math.DG↗