Related papers: On Product And Golden Structures And Harmonicity
In this article topologies on metagroups are studied. They are related with generalized $C^*$-algebras over ${\bf R}$ or ${\bf C}$. Homomorphisms and quotient maps on them are investigated. Structure of topological metagroups is…
Let $\pi:(E,\nabla^{E}) \to (M,g)$ be an affine submersion with horizontal distribution, where $\nabla^{E}$ is a symmetric connection and $M$ is a Riemannian manifold. Let $\sigma$ be a section of $\pi$, namely, $\pi \circ \sigma = Id_{M}$.…
In this article, we discuss the spaces of harmonic forms $\mathcal{H}^{\bullet}_{d}$ over a closed almost K\"{a}hler manifold $(X, J,\omega)$. We show that if the almost complex structure $J$ on the almost K\"{a}hler manifold $X$ is not too…
Hyperbolic metric and different hyperbolic type metrics are studied in open sector domains of the complex plane. Several sharp inequalities are proven for them. Our main result describes the behavior of the triangular ratio metric under…
In this paper we have discussed different possible orthogonalities in matrices, namely orthogonal, quasi-orthogonal, semi-orthogonal and non-orthogonal matrices including completely positive matrices, while giving some of their…
In this note, we survey our recent work concerning cohomologies of harmonic bundles on quasi-compact Kaehler manifolds.
Symmetries concerning the ordinary coordinate spacetime and internal spacetime are discussed. A possible unification model of electroweak, strong and gravitational interactions is briefly described.
On a 4-dimensional compact symplectic manifold, we consider a smooth family of compatible almost-complex structures such that at time zero the induced metric is Hermite-Einstein almost-K\"ahler metric with zero or negative Hermitian scalar…
Let $G=H\ltimes K$ denote a semidirect product Lie group with Lie algebra $\mathfrak g=\mathfrak h \oplus \mathfrak k$, where $\mathfrak k$ is an ideal and $\mathfrak h$ is a subalgebra of the same dimension as $\mathfrak k$. There exist…
Crystals are the materials which can be described by uniform periodic lattices. Traditionally, only the 1-, 2-, 3-, 4- and 6-fold rotation symmetries are allowed in crystals because other n-fold rotation symmetries are forbidden by the…
We investigate harmonic maps from weighted graphs into metric spaces that locally admit unique centers of gravity, like Alexandrov spaces with upper curvature bounds. We prove an existence result by constructing an iterative geometric…
We present a necessary and sufficient condition for a random product of maps on a compact metric space to be (strongly) synchronizing on average.
We study locally compact metric spaces that enjoy various forms of homogeneity with respect to M\"obius self-homeomorphisms. We investigate connections between such homogeneity and the combination of isometric homogeneity with…
Apart from not having crystallized, supercooled liquids can be considered as being properly equilibrated and thus can be described by a few thermodynamic control variables. In contrast, glasses and other amorphous solids can be arbitrarily…
In the paper the main attention is paid to conditions on algebras from a given variety which provide coincidence of their algebraic geometries. The main part here play the notions mentioned in the title of the paper.
Systems as diverse as mechanical structures assembled from elastic components, and photonic metamaterials enjoy a common geometrical feature: a sublattice symmetry. This property realizes a chiral symmetry first introduced to characterize a…
The thesis presents the subject of synthetic topology, especially with relation to metric spaces. A model of synthetic topology is a categorical model in which objects possess an intrinsic topology in a suitable sense, and all morphisms are…
We study the properties of a generalized metallic, a generalized product and a generalized complex structure induced on the generalized tangent bundle of $M$ by a metallic Riemannian structure $(J,g)$ on $M$, providing conditions for their…
We study conformal product structures on compact reducible Riemannian manifolds, and show that under a suitable technical assumption, the underlying Riemannian mani\-folds are either conformally flat, or triple products, \emph{i.e.} locally…
We construct a family of canonical connections and surrounding basic theory for almost complex manifolds that are equipped with an affine connection. This framework provides a uniform approach to treating a range of geometries. In…