Related papers: Differential calculus on `non-standard' ($h$-defor…
In \cite{LX}, the first author and the third author introduced and studied the horospherical $p$-Minkowski problem for smooth horospherically convex domains in hyperbolic space. In this paper, we introduce and solve the discrete…
A novel differential calculus with central inner product is introduced for kappa-Minkowski space. The `bad' behaviour of this differential calculus is discussed with reference to symplectic quantisation and A-infinity algebras. Using this…
In this paper, we establish various inequalities for some differentiable mappings that are linked with the illustrious Hermite- Hadamard integral inequality for mappings whose derivatives are (h -($\alpha$?;m))-convex.The generalized…
Exceptional points of a class of non-hermitian Hamilton operators $\hat H$ of the form $\hat H=\hat H_0+i\hat H_1$ are studied, where $\hat H_0$ and $\hat H_1$ are hermitian operators. Finite dimensional Hilbert spaces are considered. The…
In our previous publications we have introduced a differential calculus on the algebra $U(gl(m))$ based on a new form of the Leibniz rule which differs from that usually employed in Noncommutative Geometry. This differential calculus…
A natural extension of the standard model within non-commutative geometry is presented. The geometry determines its Higgs sector. This determination is fuzzy, but precise enough to be incompatible with experiment.
This paper studies geometric structures on noncommutative hypersurfaces within a module-theoretic approach to noncommutative Riemannian (spin) geometry. A construction to induce differential, Riemannian and spinorial structures from a…
Methods developed for the analysis of non-linear integrable models are used in the harmonic superspace (HS) framework. These methods, when applied to the HS, can lead to extract more information about the meaning of integrability in…
In this paper, we investigate the similarity transformations in the Minkowski-n space. We study the geometric invariants of non-null curves under the similarity transformations. Besides, we extend the fundamental theorem for a non-null…
We introduce a notion of the Euclidean- and the Minkowski rank for arbitrary metric spaces and we study their behaviour with respect to products. We show that the Minkowski rank is additive with respect to metric products, while additivity…
Let $M$ be a complete connected Riemannian manifold. Assuming that the Riemannian measure is doubling, we define Hardy spaces $H^p$ of differential forms on $M$ and give various characterizations of them, including an atomic decomposition.…
We review a new theory of orthogonal separation of variables on pseudo-Riemannian spaces of constant zero curvature via concircular tensors and warped products. We then apply this theory to three-dimensional Minkowski space, obtaining an…
We consider several differential operators on compact almost-complex, almost-Hermitian and almost-K\"ahler manifolds. We discuss Hodge Theory for these operators and a possible cohomological interpretation. We compare the associated spaces…
A complete Fock space representation of the covariant differential calculus on quantum space is constructed. The consistency criteria for the ensuing algebraic structure, mapping to the canonical fermions and bosons and the consequences of…
Covariant first order differential calculus over quantum complex Grassmann manifolds is considered. It is shown by a Pusz-Woronowicz type argument that under restriction to calculi close to classical Kaehler differentials there exist…
We define and study noncommutative generalizations of submanifolds and quotient manifolds, for the derivation-based differential calculus introduced by M.~Dubois-Violette and P.~Michor. We give examples to illustrate these definitions.
We clarify the relation between noncommutative spacetimes and multifractional geometries, two quantum-gravity-related approaches where the fundamental description of spacetime is not given by a classical smooth geometry. Despite their…
We show that bicovariant bimodules as defined by Woronowicz are in one to one correspondence with the Drinfeld quantum double representations. We then prove that a differential calculus associated to a bicovariant bimodule of dimension n is…
We develope a difference calculus analogous to the differential geometry by translating the forms and exterior derivatives to similar expressions with difference operators, and apply the results to fields theory on the lattice [Ref. 1]. Our…
Some Hermite-Hadamard's mid-point type inequalities related to Katugampola fractional integrals are obtained where the first derivative of considered mappings is Lipschitzian or convex. Also some mid-point type inequalities are given for…