Ray Singer torsion is a numerical invariant associated with a compact manifold equipped with a flat bundle, a Riemannian metric on the manifold and a Hermitian structure on the bundle. In this note we show how one can remove the dependence on the Riemannian metric and the Hermitian structure with the help of a base point and of an Euler structure, and obtain a topological invariant. A numerical...

In this paper we study a nonlinear elliptic system of equations imposed on a map from a complete Hermitian (non-Kähler) manifold to a Riemannian manifold. This system is more appropriate to Hermitian geometry than the harmonic map system since it is compatible with the holomorphic structure of the domain manifold in the sense that holomorphic maps are Hermitian harmonic maps. It was first studi...

In this article we consider the system of operator equations T_iX=U_i for i=1,2,...,n and give necessary and suffcient conditions for the existence of common Hermitian solutions to this system of operator equations for arbitrary operators without the closedness condition. Also we study the Moore-penrose inverse of a ncross 1 block operator matrix and. then gi...

We give an elementary proof of the fact that any 4-dimensional para-Hermitian manifold admits a unique para-Kähler–Weyl structure. We then use analytic continuation to pass from the para-complex to the complex setting and thereby show that any 4-dimensional pseudo-Hermitian manifold also admits a unique Kähler–Weyl structure.

in this paper we consider the solutions of linear systems of saddle point problems‎. ‎by using the spectrum of a quadratic matrix polynomial‎, ‎we study the eigenvalues of the iterative matrix of the hermitian and skew hermitian splitting method‎.

‎In this article we review an algebraic definition of the gyrogroup and a simplified version of the gyrovector space with two fundamental examples on the open ball of finite-dimensional Euclidean spaces‎, ‎which are the Einstein and M"{o}bius gyrovector spaces‎. ‎We introduce the structure of gyrovector space and the gyroline on the open convex cone of positive definite matrices and explore its...

One of the simplest non-Hermitian Hamiltonians, first proposed by Schwartz in 1960, that may possess a spectral singularity is analysed from the point of view of the non-Hermitian generalization of quantum mechanics. It is shown that the η operator, being a second-order differential operator, has supersymmetric structure. Asymptotic behaviour of the eigenfunctions of a Hermitian Hamiltonian equ...

In this paper we derive canonical forms under structure preserving equivalence transformations for matrices and matrix pencils that have a multiple structure, which is either an H-selfadjoint or H-skew-adjoint structure, where the matrix H is a complex nonsingular Hermitian or skew-Hermitian matrix. Matrices and pencils of such multiple structures arise for example in quantum chemistry in Hartr...

We investigate the classical limit of non-Hermitian quantum dynamics arising from a coherent state approximation, and show that the resulting classical phase space dynamics can be described by generalised “canonical” equations of motion, for both conservative and dissipative motion. The dynamical equations combine a symplectic flow associated with the Hermitian part of the Hamiltonian with a me...