We show that if the Stokes matrix of a connection with a pole of order two and no ramification gives rise, when added to its adjoint, to a positive semi-definite Hermitian form, then the associated integrable twistor structure (or TERP structure, or non-commutative Hodge structure) is pure and polarized.

We derive the loop equations for the one Hermitian matrix model in any dimension. These are a consequence of the Schwinger-Dyson equations of the model. Moreover we show that in leading order of large N the loop equations form a closed set. CERN–TH-6966/93 August 1993 ∗Permanent address: Fac. de F́ısica, Universidad Católica de Chile, Casilla 306, Santiago 22, Chile.

Let E : 0 → S → E → Q → 0 be a short exact sequence of hermitian vector bundles with metrics on S and Q induced from that on E. We compute the Bott-Chern form φ̃(E ) corresponding to any characteristic class φ, assuming E is projectively flat. The result is used to obtain a new presentation of the Arakelov Chow ring of the arithmetic Grassmannian.

Let {φn} be a sequence of rational functions with arbitrary complex poles, generated by a certain three-term recurrence relation. In this paper we show that under some mild conditions, the rational functions φn form an orthonormal system with respect to a Hermitian positive-definite inner product.

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.

Let {φn} be a sequence of rational functions with arbitrary complex poles, generated by a certain three-term recurrence relation. In this paper we show that under some mild conditions the rational functions φn form an orthonormal system with respect to a Hermitian positive-definite inner product.

In arXiv:0709.0483 Günther and Samsonov outline a “generalization” of quantum mechanics that involves simultaneous consideration of Hermitian and non-Hermitian operators and promises to be “capable to produce effects beyond those of standard Hermitian quantum mechanics.” We give a simple physical interpretation of Hermiticity and discuss in detail the shortcomings of the above-mentioned composi...

The classical second order Lamé equation contains a so-called accessory parameter B. In this paper we study for which values of B the Lamé equation has a monodromy group which is conjugate to a subgroup of SL(2,R) (unitary monodromy with indefinite hermitian form). We refomulate the problem as a spectral problem and give an asymptotic expansion for the spectrum.

We describe all almost contact metric, almost hermitian and G 2-structures admitting a connection with totally skew-symmetric torsion tensor, and prove that there exists at most one such connection. We investigate its torsion form, its Ricci tensor, the Dirac operator and the ∇-parallel spinors. In particular, we obtain solutions of the type II string equations in dimension n = 5, 6 and 7.

Geometric quantization on a coset space G/H is considered, intending to recover Mackey’s inequivalent quantizations. It is found that the inequivalent quantizations can be obtained by adopting the symplectic 2-form which leads to Wong’s equation. The irreducible representations of H which label the inequivalent quantizations arise from Weil’s theorem, which ensures a Hermitian bundle over G/H t...