Related papers: Spectral Bounds for Dirac Operators on Open Manifo…

We show that on every compact spin manifold admitting a Riemannian metric of positive scalar curvature Friedrich's eigenvalue estimate for the Dirac operator can be made sharp up to an arbitrarily small given error by choosing the metric…

In K\"ahler-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…

We prove a lower estimate for the first eigenvalue of the Dirac operator on a compact locally reducible Riemannian spin manifold with positive scalar curvature. We determine also the universal covers of the manifolds on which the smallest…

We consider the Dirac operator on compact quaternionic Kaehler manifolds and prove a lower bound for the spectrum. This estimate is sharp since it is the first eigenvalue of the Dirac operator on the quaternionic projective space.

We prove a lower bound for the first eigenvalue of the Dirac operator on a compact Riemannian spin manifold depending on the scalar curvature as well as a chosen Codazzi tensor. The inequality generalizes the classical estimate from [2].

In this paper, we get estimates on the higher eigenvalues of the Dirac operator on locally reducible Riemannian manifolds, in terms of the eigenvalues of the Laplace-Beltrami operator and the scalar curvature. These estimates are sharp, in…

We get optimal lower bounds for the eigenvalues of the submanifold Dirac operator on locally reducible Riemannian manifolds in terms of intrinsic and extrinsic expressions. The limiting-cases are also studied. As a corollary, one gets…

In this note, we prove lower and upper bounds for Dirac operators of submanifolds in certain ambient manifolds in terms of conformal and extrinsic quantities.

In this paper we will prove new extrinsic upper bounds for the eigenvalues of the Dirac operator on an isometrically immersed surface $M^2 \hookrightarrow {\Bbb R}^3$ as well as intrinsic bounds for 2-dimensional compact manifolds of genus…

We give lower bounds for the eigenvalues of the submanifold Dirac operator in terms of intrinsic and extrinsic curvature expressions. We also show that the limiting cases give rise to a class generalizing that of Killing spinors. We…

In this article, we study the spectrum of the magnetic Dirac operator, and the magnetic Dirac operator with potential over complete Riemannian manifolds. We find sufficient conditions on the potentials as well as the manifold so that the…

We get optimal lower bounds for the eigenvalues of the Dirac-Witten operator on locally reducible spacelike submanifold in terms of intrinsic and extrinsic expressions. The limiting-cases are also studied.

Under standard local boundary conditions or certain global APS boundary conditions, we get lower bounds for the eigenvalues of the Dirac operator on compact spin manifolds with boundary. Limiting cases are characterized by the existence of…

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 special case of Einstein manifolds, we obtain estimates depending…

It has recently been conjectured that the eigenvalues $\lambda$ of the Dirac operator on a closed Riemannian spin manifold $M$ of dimension $n\ge 3$ can be estimated from below by the total scalar curvature: $$ \lambda^2 \ge…

We prove a new lower bound for the first eigenvalue of the Dirac operator on a compact Riemannian spin manifold by refined Weitzenb\"ock techniques. It applies to manifolds with harmonic curvature tensor and depends on the Ricci tensor.…

Using Weitzenb\"ock 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…

We derive new lower bounds for the first eigenvalue of the Dirac operator of an oriented hypersurface $\Sigma$ bounding a noncompact domain in a spin asymptotically flat manifold (M n , g) with nonnegative scalar curvature. These bounds…

In this paper, we consider the eigenvalue problem of Dirac operator on a compact Riemannian manifold isometrically immersed into Euclidean space and derive some extrinsic estimates for the sum of arbitrary consecutive $n$ eigenvalues of the…

For closed connected Riemannian spin manifolds an upper estimate of the smallest eigenvalue of the Dirac operator in terms of the hyperspherical radius is proved. When combined with known lower Dirac eigenvalue estimates, this has a number…