Related papers: A Gutzwiller type trace formula for the magnetic D…

In this paper, we give two Lichnerowicz type formulas for Dirac operators and signature operators twisted by a vector bundle with a non-unitary connection. We also prove two Kastler-Kalau-Walze type theorems for twisted Dirac operators and…

In this article, we prove a Sobolev-like inequality for the Dirac operator on closed compact Riemannian spin manifolds with a nearly optimal Sobolev constant. As an application, we give a criterion for the existence of solutions to a…

We establish an index theorem for Toeplitz operators on odd dimensional spin manifolds with boundary. It may be thought of as an odd dimensional analogue of the Atiyah-Patodi-Singer index theorem for Dirac operators on manifolds with…

We give a relativistic generalization of the Gutzwiller-Duistermaat-Guillemin trace formula for the wave group of a compact Riemannian manifold to globally hyperbolic stationary space-times with compact Cauchy hypersurfaces. We introduce…

In [10], Dabrowski etc. gave spectral Einstein bilinear functionals of differential forms for the Hodge-Dirac operator $d+\delta$ on an oriented even-dimensional Riemannian manifold. In this paper, we generalize the results of Dabrowski…

We find Weitzenb\"ock formula for the Fueter-Dirac operator which controls the infinitesimal deformations of an associative submanifold in a $7$--manifold with a $G_2$--structure. We establish a vanishing theorem to conclude rigidity under…

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…

Using the Arthur-Selberg trace formula we express the index of a Dirac operator on an arithmetic quotient over a totally real field with at least two real embeddings as the integral over the index form plus a sum of orbital integrals. For…

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.…

Several proofs have been published of the Mod Z gluing formula for the eta-invariant of a Dirac operator. However, so far the integer contribution to the gluing formula for the eta-invariant is left obscure in the literature. In this…

We prove an adiabatic decomposition formula of the zeta-determinant of the Laplace type operator with respect to Dirichlet boundary condition. We allow the non-invertible tangential operator. As a result, our adiabatic decomposition formula…

Gutzwiller's trace formula for the semiclassical density of states diverges at the bifurcation points of periodic orbits and has to be replaced with uniform semiclassical approximations. We present a method to derive these expressions from…

Assume that the compact Riemannian spin manifold $(M^n,g)$ admits a $G$-structure with characteristic connection $\nabla$ and parallel characteristic torsion ($\nabla T=0$), and consider the Dirac operator $D^{1/3}$ corresponding to the…

We consider self-adjoint fourth order operators on the unit interval with the Dirichlet type boundary conditions. For such operators we determine few trace formulas, similar to the case of Gelfand--Levitan formulas for second order…

We prove an extension to R^n, endowed with a suitable metric, of the relation between the Einstein-Hilbert action and the Dirac operator which holds on closed spin manifolds. By means of complex powers, we first define the regularised…

Let X be a compact manifold with boundary, and suppose that the boundary is the total space of a fibration with base Y and fibre Z. Let D be a generalized Dirac operator associated to a Phi-metric g on X. Under the assumption that D is…

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…

We show meromorphic extension and analyze the divisors of a Selberg zeta function of odd type $Z_{\Gamma,\Sigma}^{\rm o}(\lambda)$ associated to the spinor bundle $\Sigma$ on odd dimensional convex co-compact hyperbolic manifolds…

In this paper we investigate the properties of a semi-linear problem on a spin manifold involving the Dirac operator, through the construction of Rabinowitz-Floer homology groups. We give several existence results for sub-critical and…

In this work we consider the $\eta$-invariant for pseudodifferential operators of tensor product type, also called bisingular pseudodifferential operators. We study complex powers of classical bisingular operators. We prove the trace…