Related papers: Almost Hermitian Identities

In infinite-dimensional Hilbert spaces, the application of the concept of quasi-Hermiticity to the description of non-Hermitian Hamiltonians with real spectra may lead to problems related to the definition of the metric operator. We discuss…

In the case where both the domain and target manifolds are almost Hermitian, we introduce the concept of Hermitian pluriharmonic maps. We prove that any holomorphic or anti-holomorphic map between almost Hermitian manifolds is Hermitian…

We explore the relationship between approximate symmetries of a gapped Hamiltonian and the structure of its ground space. We start by showing that approximate symmetry operators---unitary operators whose commutators with the Hamiltonian…

We show that the de Rham complex of any almost Hermitian manifold carries a natural commutative $BV_\infty$-algebra structure satisfying the degeneration property. In the almost K\"ahler case, this recovers Koszul's BV-algebra, defined for…

A quasi-Hermitian operator is an operator that is similar to its adjoint in some sense, via a metric operator, i.e., a strictly positive self-adjoint operator. Whereas those metric operators are in general assumed to be bounded, we analyze…

The principal aim of this paper is to derive an abstract form of the third Green identity associated with a proper extension $T$ of a symmetric operator $S$ in a Hilbert space $\mathfrak H$, employing the technique of quasi boundary triples…

Motivated by the recent developments of pseudo-Hermitian quantum mechanics, we analyze the structure generated by unbounded metric operators in a Hilbert space. To that effect, we consider the notions of similarity and quasi-similarity…

We consider strict and complete nearly Kaehler manifolds with the canonical Hermitian connection. The holonomy representation of the canonical Hermitian connection is studied. We show that a strict and complete nearly Kaehler is locally a…

The subject of this paper is six-dimensional nearly (para-)K\"ahler geometry with pseudo-Riemannian metrics. Firstly, we derive the analogue of the well-known exterior differential system characterising a nearly K\"ahler manifold and prove…

Tubular neighborhoods play an important role in differential topology. We have applied these constructions to geometry of almost Hermitian manifolds. At first, we consider deformations of tensor structures on a normal tubular neighborhood…

We characterize quasi K\"ahler manifolds whose curvature tensor associated to the canonical Hermitian connection satisfies the first Bianchi identity. This condition is related with the third Gray identity and in the almost K\"ahler case…

We define naturally Hermite-Lorentz metrics on almost-complex manifolds as special case of pseudo-Riemannian metrics compatible with the almost complex structure. We study their isometry groups.

We survey the theory of locally homogeneous almost-Hermitian spaces. In particular, by using the framework of varying Lie brackets, we write formulas for the curvature of all the Gauduchon connections and we provide explicit examples of…

In this paper, by introducing a notion of local quasi holomorphic frame, we obtain a curvature formula for almost Hermitian manifolds which is similar to that of Hermitian manifolds. Moreover, as applications of the curvature formula, we…

This paper demonstrates the power of the calculus developed in the two previous parts of the series for all real forms of the almost Hermitian symmetric structures on smooth manifolds, including e.g. conformal Riemannian and almost…

We get several identities of differential operators in determinantal form. These identities are non-commutative versions of the formula of Cauchy-Binet or Laplace expansions of determinants, and if we take principal symbols, they are…

On an almost Hermitian manifold, we have two Hermitian scalar curvatures with respect to any canonical Hermitian connection defined by P. Gauduchon. Explicit formulas of these two Hermitian scalar curvatures are obtained in terms of…

We analyze an approximation of a Laplacian subject to non-local interface conditions of a $\delta'$-type by Neumann Laplacians on a family of Riemannian manifolds with a sieve-like structure. We establish a (kind of) resolvent convergence…

We study almost Hermitian structures admitting a Hermitian connexion with totally skew-symmetric torsion or equivalently, those almost Hermitian structures with totally skew-symmetric Nijenhuis tensor. We investigate up to what extent the…

The purpose of the article is to generalize the concept of approximate Birkhoff-James orthogonality, in the semi-Hilbertian structure. Given a positive operator $ A $ on a Hilbert space $ \mathbb{H}, $ we define $ (\epsilon,A)- $approximate…