Structured rational matrices such as symmetric, skew-symmetric, Hamiltonian, skew-Hamiltonian, Hermitian, and para-Hermitian arise in many applications. Linearizations of rational...

We develop a duality theory for unbounded Hermitian operators with dense domain in Hilbert space. As is known, the obstruction for a Hermitian operator to be selfadjoint or to have selfadjoint extensions is measured by a pair of deficiency indices, and associated deficiency spaces; but in practical problems, the direct computation of these indices can be difficult. Instead, in this paper we ide...

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...

A conformal change of TM ⊕ T ∗M is a morphism of the form (X,α) 7→ (X, eτα) (X ∈ TM,α ∈ T ∗M, τ ∈ C∞(M)). We characterize the generalized almost complex and almost Hermitian structures that are locally conformal to integrable and to generalized Kähler structures, respectively, and give examples of such structures.

We study some similarities between almost product Riemannian structures and almost Hermitian structures. Inspired by the similarities, we prove lower eigenvalue estimates for the Dirac operator on compact Riemannian spin manifolds with locally product structures. We also provide some examples (limiting manifolds) for the limiting case of the estimates. MSC(2000): 53C25, 53C27, 58B20

s 19 ALEKSEEVSKY, Dmitri , Geometry of quaternionic and para-quaternionic CR manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 BELKO, Ivan, The fundamental form on a Lie groupoid of diffeomorphisms 20 BOGDANOVICH, Sergey A., ERMOLITSKI, Alexander A., Hypercomplex structures on tangent bundles . . . . . . . . . . . . . . . . . . . . 22 DESZCZ, Ryszard, On Roter type mani...

We introduce the notion of even Clifford structures on Riemannian manifolds, which for rank r = 2 and r = 3 reduce to almost Hermitian and quaternion-Hermitian structures respectively. We give the complete classification of manifolds carrying parallel rank r even Clifford structures: Kähler, quaternion-Kähler and Riemannian products of quaternion-Kähler manifolds for r = 2, 3 and 4 respectively...

We develop relativistic wave equations in the framework of the new non-hermitian PT quantum mechanics. The familiar Hermitian Dirac equation emerges as an exact result of imposing the Dirac algebra, the criteria of PT -symmetric quantum mechanics, and relativistic invariance. However, relaxing the constraint that in particular the mass matrix be Hermitian also allows for models that have no cou...