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Let G/H be a pseudo-Riemannian semisimple symmetric space. The tangent bundle T(G/H) contains a maximal G-invariant neighbourhood of the zero section where the adapted complex structure exists. Such neighbourhood is endowed with a canonical…

We analyze the sharpness of the Sobolev order for left-invariant vector fields on compact Riemannian manifolds. Utilizing techniques from pseudo-differential operator theory and microlocal analysis, we investigate the asymptotic behavior of…

We consider a subanalytic subset A of a complex analytic manifold M (when M is viewed as a real manifold) and formulate conditions under which A is a complex analytic subset of M.

The proposed coordinate/field duality [Phys. Rev. Lett. 78 (1997) 163] is applied to the gauge and matter sectors of gauge theories. In the non-Abelian case, due to indices originated from the internal space, the dual coordinates appear to…

This is the second of a series of papers outlining an approach to the classification of $\mathcal{N}{=}2$ superconformal field theories at rank 2 via a systematic analysis of their Coulomb branches, mathematically described by special…

On a Hermitian manifold we construct a symmetric $(1,1)$- tensor $H$ using the torsion and the curvature of the Chern connection. On a compact balanced Hermitian manifold we find necessary and sufficient conditions in terms of the tensor…

Correlation is a common technique for the detection of shifts. Its generalization to the multidimensional geometric correlation in Clifford algebras additionally contains information with respect to rotational misalignment. It has been…

The purpose of this paper is to put the description of number scaling and its effects on physics and geometry on a firmer foundation, and to make it more understandable. A main point is that two different concepts, number and number value…

We present a new formulation of some basic differential geometric notions on a smooth manifold M, in the setting of nonstandard analysis. In place of classical vector fields, for which one needs to construct the tangent bundle of M, we…

New splitting theorems in a semi-Riemannian manifold which admits an irrotational vector field (not necessarily a gradient) with some suitable properties are obtained. According to the extras hypothesis assumed on the vector field, we can…

Let $(M,\omega)$ be an almost symplectic manifold ($\omega$ is a non degenerate, not closed, 2-form). We say that a vector field $X$ of $M$ is locally Hamiltonian if $L_X\omega=0,d(i(X)\omega)=0$, and it is Hamiltonian if, furthermore, the…

We investigate the conditions under which cosmological variations in physical `constants' and scalar fields are detectable on the surface of local gravitationally-bound systems, such as planets, in non-spherically symmetric background…

We prove that the set of orthogonal separable coordinates on an arbitrary (pseudo-)Riemannian manifold carries a natural structure of a projective variety, equipped with an action of the isometry group. This leads us to propose a new,…

We consider the linear space of composite fields as an infinite dimensional vector bundle over the theory space whose coordinates are simply the parameters of a renormalized field theory. We discuss a geometrical expression for the short…

We apply the graph complex method to vector fields depending naturally on a set of vector fields and a linear symmetric connection. We characterize all possible systems of generators for such vector-field valued operators including the…

We begin by showing that every real analytic orbifold has a real analytic Riemannian metric. It follows that every reduced real analytic orbifold can be expressed as a quotient of a real analytic manifold by a real analytic almost free…

This article studies the smoothness of conformal mappings between two Riemannian manifolds whose metric tensors have limited regularity. We show that any bi-Lipschitz conformal mapping or $1$-quasiregular mapping between two manifolds with…

Indices of vector fields on (complex analytic) singular varieties have been considered by various authors from several different viewpoints. All these indices coincide with the classical local index of Poincar\'e-Hopf when the ambient…

Usually, the description of tangent spaces to the Teichmueller space $\mathscr{T}(\Sigma_{g})$ of a compact Riemann surface $\Sigma_{g}$ of genus $g \geq 2$ (which we can identify with the quotient space $\mathbb{H}^{2} / \Gamma_{g}$ of the…

We find a principle of harmonic analyticity underlying the quaternionic (quaternion-K\"ahler) geometry and solve the differential constraints which define this geometry. To this end the original $4n$-dimensional quaternionic manifold is…