Related papers: Almost Hermitian Identities

We study $\mathcal D$-homothetic deformations of almost $\alpha$-Kenmotsu structures. We characterize almost contact metric manifolds which are $CR$-integrable almost $\alpha$-Kenmotsu manifolds, through the existence of a canonical linear…

We study some properties of pointwise $k$-slant submanifolds of almost Hermitian manifolds with a special view towards K\"{a}hler manifolds. In particular, we characterize the integrability of the component distributions, treating also the…

We give a partial account of some problems concerning cohomological invariants and metric properties of complex non-K\"ahler manifolds.

Let J be a unitary almost complex structure on a Riemannian manifold (M,g). If x is a unit tangent vector, let P be the associated complex line spanned by x and by Jx. We show that if (M,g) is Hermitian or if (M,g) is nearly Kaehler, then…

Let $(\acute{N},g,\nabla )$\ be a $2n$-dimensional quasi-statistical manifold that admits a pseudo-Riemannian metric $g$ (or $h)$ and a linear connection $\nabla $ with torsion. This paper aims to study an almost Hermitian structure $(g,L)$…

The characteristic connection of an almost hermitian structure is a hermitian connection with totally skew-symmetric torsion. The case of parallel torsion in dimension six is of particular interest. In this work, we give a full…

This paper focuses on properties of \partial-biLipschitz mappings which were recently introduced by Bulter. We establish several characterizations for the class of \partial-biLipschitz mappings between domains in quasiconvex metric spaces.…

Let $(G,g)$ be a 4-dimensional Riemannian Lie group with a 2-dimensional left-invariant, conformal foliation $\F$ with minimal leaves. Let $J$ be an almost Hermitian structure on $G$ adapted to the foliation $\F$. We classify such…

Consider a fractional operator $P^s$, $0<s<1$, for connection Laplacian $P:=\nabla^*\nabla+A$ on a smooth Hermitian vector bundle over a closed, connected Riemannian manifold of dimension $n\geq 2$. We show that local knowledge of the…

The problem of determining the domain of the closure of the Laplace-Beltrami operator on a 2D almost-Riemannian manifold is considered. Using tools from theory of Lie groupoids natural domains of perturbations of the Laplace-Beltrami…

The subject of investigations are the almost hypercomplex manifolds with Hermitian and anti-Hermitian (Norden) metrics. A linear connection D is introduced such that the structure of these manifolds is parallel with respect to D and its…

In this paper we study invariant almost Hermitian geometry on generalized flag manifolds. We will focus on providing examples of K\"ahler like scalar curvature metric, that is, almost Hermitian structures $(g,J)$ satisfying $s=2s_{\rm C}$,…

Almost para-Hermitian manifold it is manifold equipped with almost para-complex structure and compatible pseudo-metric of neutral signature. It is considered a class of immersions of almost para-Hermitian manifolds into almost…

Almost hypercomplex manifolds with Hermitian and anti-Hermitian metrics are considered. A linear connection $D$ is introduced such that the structure of these manifolds is parallel with respect to D. Of special interest is the class of the…

We give an explicit characterization of the most general quasi-Hermitian operator H, the associated metric operators \eta_+, and \eta_+-pseudo-Hermitian operators acting in two-dimensional complex Euclidean space C^2. These operators…

This paper is a study of almost contact statistical manifolds. Especially this study is focused on almost cosymplectic statistical manifolds. We obtained basic properties of such manifolds. It is proved a characterization theorem and a…

We study curvature properties of four-dimensional almost Hermitian manifolds with vanishing Bochner curvature tensor as defined by Tricerri and Vanhecke. We give local structure theorems for such Kaehler manifolds, and find out several…

Quasi-Hermitian quantum systems, including $\mathcal{PT}$-symmetric ones, can be mapped to equivalent Hermitian systems via a similarity transformation that redefines the inner product with a positive-definite metric operator. Although an…

In this paper, we consider a non-degenerate CR manifold (M,H(M),J) with a given pseudo-Hermitian 1-form {\theta}, and endow the CR distribution H(M) with any Hermitian metric h instead of the Levi form L_{{\theta}}. This induces a natural…

Suppose two Hermitian matrices $A,B$ almost commute ($\Vert [A,B] \Vert \leq \delta$). Are they close to a commuting pair of Hermitian matrices, $A',B'$, with $\Vert A-A' \Vert,\Vert B-B'\Vert \leq \epsilon$? A theorem of H. Lin shows that…