相关论文: Spectral Torsion for Nonminimal de-Rham Hodge Oper…

The behaviour of the spectral edges (embedded eigenvalues and resonances) is discussed at the two ends of the continuous spectrum of non-local discrete Schr\"odinger operators with a $\delta$-potential. These operators arise by replacing…

We define two types of pseudo-differential perturbations of the Dirac operator within the framework of the noncommutative geometry. And we obtain the noncommutative residue of the inverse square of these perturbations on 4-dimensional…

The differential-geometric and topological structure of Delsarte transmutation operators and associated with them Gelfand-Levitan-Marchenko type eqautions are studied making use of the De Rham-Hodge-Skrypnik differential complex. The…

This is a survey article on a known generalization of Dirac-type operators to transverse operators called basic Dirac operators on Riemannian foliations, which are smooth foliations that have a transverse geometric structure. Construction…

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 define the spectral Einstein functional associated with the sub-Dirac operator for manifolds with boundary. A proof of the Dabrowski-Sitarz-Zalecki type theorem for spectral Einstein functions associated with the sub-Dirac…

In this paper, we get the Kastler-Kalau-Walze theorem associated to Dirac operators with torsion on compact manifolds with boundary. We give two kinds of operator-theoretic explanations of the gravitational action in the case of…

The aim of the lectures is to introduce first-year Ph.D. students and research workers to the theory of the Dirac operator, spinor techniques, and their relevance for the theory of eigenvalues in Riemannian geometry. Topics: differential…

We construct invariant differential operators acting on sections of vector bundles of densities over a smooth manifold without using a Riemannian metric. The spectral invariants of such operators are invariant under both the diffeomorphisms…

We study a natural Dirac operator on a Lagrangian submanifold of a K\"ahler manifold. We first show that its square coincides with the Hodge-de Rham Laplacian provided the complex structure identifies the Spin structures of the tangent and…

We study Dirac-harmonic maps from surfaces to manifolds with torsion, which is motivated from the superstring action considered in theoretical physics. We discuss analytic and geometric properties of such maps and outline an existence…

In this paper we consider the Dirac spinor field in interaction with a background of electrodynamics and torsion-gravity; by performing the polar reduction we acquire the possibility to introduce a new set of objects that have the…

We compute the spectrum of the Dirac operator on 3-dimensional Heisenberg manifolds. The behavior under collapse to the 2-torus is studied. Depending on the spin structure either all eigenvalues tend to $\pm\infty$ or there are eigenvalues…

Spectral (Bloch) varieties of multidimensional differential operators on non-simply connected manifolds are defined. In their terms it is given a description of the analytical dependence of the spectra of magnetic Laplacians on non-simply…

In this paper, we prove the invariance of the spectrum of the basic Dirac operator defined on a Riemannian foliation $(M,\mathcal{F})$ with respect to a change of bundle-like metric. We then establish new estimates for its eigenvalues on…

When aiming to apply mathematical results of non-commutative geometry to physical problems the question arises how they translate to a context in which only a part of the spectrum is known. In this article we aim to detect when a…

A review on spectral and differential-geometric properties of Delsarte transmutation operators in multidimension is given. Their differential geometrical and topological structure in multidimension is analyzed, the relationships with De…

A Dirac operator is presented that will yield a 1+ summable regular even spectral triple for all noncommutative compact surfaces defined as subalgebras of the Toeplitz algebra. Connes' conditions for noncommutative spin geometries are…

Let $\Omega$ be an unbounded two dimensional strip on a ruled surface in $\mathbb{R}^d$, $d\geq2$. Consider the Laplacian operator in $\Omega$ with Dirichlet and Neumann boundary conditions on opposite sides of $\Omega$. We prove some…

We introduce a non-backtracking Laplace operator for graphs and we investigate its spectral properties. With the use of both theoretical and computational techniques, we show that the spectrum of this operator captures several structural…