相关论文: The spectrum of twisted Dirac operators on compact…

We present a new description of the spectrum of the (spin-) Dirac operator $D$ on lens spaces. Viewing a spin lens space $L$ as a locally symmetric space $\Gamma\backslash \operatorname{Spin}(2m)/\operatorname{Spin}(2m-1)$ and exploiting…

We obtain a simple formula for the multiplicity of eigenvalues of the Hodge-Laplace operator, $\Delta_f$, acting on sections of the full exterior bundle over an arbitrary compact flat Riemannian n-manifold M with holonomy group Z_2^k, with…

In the setting of a proper, cocompact action by a locally compact, unimodular group $G$ on a Riemannian manifold, we construct equivariant spectral flow of paths of Dirac-type operators. This takes values in the $K$-theory of the group…

Given a closed connected spin manifold M with non-negative and somewhere positive scalar curvature, we show that the Dirac operator twisted with any flat Hilbert module bundle is invertible.

Starting from an even definite lattice, we construct a principal circle bundle covered by a certain three-step nilpotent Lie group G. On the base space, which is again a nilmanifold, we then study the Dirac operator twisted by the…

It is known that, for Dirac operators on Riemann surfaces twisted by line bundles with Hermitian-Einstein connections, it is possible to obtain estimates for the first eigenvalue in terms of the topology of the twisting bundle \cite{JL2}.…

We determine the structure of conformal powers of the Dirac operator on Einstein {\it Spin}-manifolds in terms of the product formula for shifted Dirac operators. The result is based on the techniques of higher variations for the Dirac…

We establish a lower bound for the eigenvalues of the Dirac operator defined on a compact K\"ahler-Einstein manifold of positive scalar curvature and endowed with particular ${\rm spin}^c$ structures. The limiting case is characterized by…

The interaction between spin geometry and positive scalar curvature has been extensively explored. In this paper, we instead focus on Dirac operators on Riemannian three-manifolds for which the spectral gap $\lambda_1^*$ of the Hodge…

We derive an inequality that relates nodal set and eigenvalues of a class of twisted Dirac operators on closed surfaces and point out how this inequality naturally arises as an eigenvalue estimate for the $\rm Spin^c$ Dirac operator. This…

In this paper, we describe the group SpinT (n) and give some properties of this group. We construct SpinT spinor bundle S by means of the spinor representation of the group SpinT (n) and define covariant derivative operator and Dirac…

The issue of general covariance of spinors and related objects is reconsidered. Given an oriented manifold $M$, to each spin structure $\sigma$ and Riemannian metric $g$ there is associated a space $S_{\sigma, g}$ of spinor fields on $M$…

We present a universal Dirac operator for noncommutative spin and spin^c bundles over fuzzy complex projective spaces. We give an explicit construction of these bundles, which are described in terms of finite dimensional matrices, calculate…

Consider the massless Dirac operator on a 3-torus equipped with Euclidean metric and standard spin structure. It is known that the eigenvalues can be calculated explicitly: the spectrum is symmetric about zero and zero itself is a double…

Given a compact Riemannian spin manifold with positive scalar curvature, we find a family of connections $\nabla^{A_t}$ for $t\in[0,1]$ on a trivial vector bundle of sufficiently high rank, such that the first eigenvalue of the twisted…

Along the lines of the classic Hodge-De Rham theory a general decomposition theorem for sections of a Dirac bundle over a compact Riemannian manifold is proved by extending concepts as exterior derivative and coderivative as well as as…

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…

On a compact spin manifold we study the space of Riemannian metrics for which the Dirac operator is invertible. The first main result is a surgery theorem stating that such a metric can be extended over the trace of a surgery of codimension…

We study the behavior of the spectrum of the Dirac operator on degenerating families of compact Riemannian surfaces, when the length $t$ of a simple closed geodesic shrinks to zero, under the hypothesis that the spin structure along the…

We consider Dirac operators on odd-dimensional compact spin manifolds which are twisted by a product bundle. We show that the space of connections on the twisting bundle which yield an invertible operator has infinitely many connected…