Related papers: On the eigenvalues of the twisted Dirac operator

For closed manifolds endowed with a Riemannian foliation of codimension $4$, one can define a transversal Seiberg-Witten map. We show that there is a finite dimensional approximation for such a map. By such a method and under the condition…

We give a new estimate on the lower bound for the first Dirichlet eigenvalue for a compact manifold with positive Ricci curvature in terms of the in-diameter and the lower bound of the Ricci curvature. The result improves the previous…

We study the index bundle of the Dirac-Ramond operator associated with a family $\pi: Z \to X$ of compact spin manifolds. We view this operator as the formal twisted Dirac operator $\dd \otimes \bigotimes_{n=1}^{\infty}S_{q^n}TM_{\C}$ so…

We shall give a twisted Dirac structure on the space of irreducible connections on a SU(n)-bundle over a three-manifold, and give a family of twisted Dirac structures on the space of irreducible connections on the trivial SU(n)-bundle over…

Let $Y$ be a compact, oriented 3-manifold with a contact form $a$ and a metric $ds^2$. Suppose that $F\to Y$ is a principal bundle with structure group $U(2) = SU(2)\times_{\pm1}S^1$ such that $F/S^1$ is the principal SO(3) bundle of…

We study sub-Dirac operators that are associated with left-invariant bracket-generating sub-Riemannian structures on compact quotients of nilpotent semi-direct products $G=\mathbb{R}^n\rtimes_A\mathbb{R}$. We will prove that these operators…

In this paper, we introduce several new secondary invariants for Dirac operators on a complete Riemannian manifold with a uniform positive scalar curvature metric outside a compact set and use these secondary invariants to establish a…

We consider the Dirac operator on right triangles, subject to infinite-mass boundary conditions. We conjecture that the lowest positive eigenvalue is minimised by the isosceles right triangle both under the area or perimeter constraints. We…

We define (higher rank) spinorially twisted spin structures and deduce various curvature identites as well as estimates for the eigenvalues of the corresponding twisted Dirac operators.

We assume that the manifold with boundary, X, has a Spin_C-structure with spinor bundle S. Along the boundary, this structure agrees with the structure defined by an infinite order integrable almost complex structure and the metric is…

We revisit the problem of determining the zero modes of the Dirac operator on the Eguchi-Hanson space. It is well known that there are no normalisable zero modes, but such zero modes do appear when the Dirac operator is twisted by a $U(1)$…

A formula is given in terms of secondary characteristic classes for the leading order contribution to the spectral flow for a path of twisted Dirac operators on an odd dimensional, Riemannian manifold when the twisting is done by a path of…

We give a formula for the first eigenvalue of the Dirac operator acting on spinor fields of a spin compact irreducible symmetric space $G/K$.

We prove asymptotically optimal upper bounds for the eigenvalues of the Wentzel-Laplace operator on Riemannian manifolds with Ricci curvature bounded below. These bounds depend highly on the geometry of the boundary in addition to the…

We analyze the low-lying spectrum and eigenmodes of lattice Dirac operators with a twisted mass term. The twist term expels the eigenvalues from a strip in the complex plane and all eigenmodes obtain a non-vanishing matrix element with…

In this paper, we estimate the eigenvalues of the twisted Dirac operator on K\"ahler submanifolds of the complex projective space $CP^m$ and we discuss the sharpness of this estimate for the embedding $CP^d \hookrightarrow CP^m$.

The twisted suspension of a manifold is obtained by surgery along the fibre of a principal circle bundle over the manifold. It generalizes the spinning operation for knots and preserves various topological properties. In this article, we…

In this paper we prove an initial data rigidity result \`a la Eichmair, Galloway and Mendes (arXiv:2009.09527) using Dirac operator techniques. It applies to initial data sets on spin bands that satisfy the dominant energy condition, a…

This paper develops a weighted $L^2$-method for the (half) Dirac equation. For Dirac bundles over closed Riemann surfaces, we give a sufficient condition for the solvability of the (half) Dirac equation in terms of a curvature integral.…

We study the behavior of the spectrum of the Dirac operator together with a symmetric $W^{1, \infty}$-potential on spin manifolds under a collapse of codimension one with bounded sectional curvature and diameter. If there is an induced spin…