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In this paper we will introduce a new notion of geometric structures defined by systems of closed differential forms in term of the Clifford algebra of the direct sum of the tangent bundle and the cotangent bundle on a manifold. We develop…

This is the second in a series of papers discussing in the framework of gerbe theory canonical and geometric aspects of the 2d nonlinear sigma model in the presence of conformal defects in the worldsheet. Employing the formal tools worked…

Let $G/H$ be a Riemannian homogeneous space. For an orthogonal representation $\phi$ of $H$ on the Euclidean space $\mathbb{R}^{k+1}$, there corresponds the vector bundle $E=G\times_{\phi}\mathbb{R}^{k+1} \to G/H$ with fiberwise inner…

To every Fell bundle $\mathscr C$ over a locally compact group ${\sf G}$ one associates a Banach $^*$-algebra $L^1({\sf G}\,\vert\,\mathscr C)$. We prove that it is symmetric whenever ${\sf G}$ with the discrete topology is rigidly…

Deep indentation of soft materials is ubiquitous across scales in nature and engineering, yet accurate predictions of contact behaviors under extreme deformations ($\delta/R > 1$) remain elusive due to geometric and material nonlinearities.…

All spherically symmetric Riemannian metrics of constant scalar curvature in any dimension can be written down in a simple form using areal coordinates. All spherical metrics are conformally flat, so we search for the conformally flat…

Using a 5-dimensional perspective, we balance algebraic and geometric handle cancellation to show that doubles of Gluck twists of certain 2-spheres with two minima are standard. This includes all 2-spheres which are unions of ribbon discs,…

We study compactifications on ${\rm AdS}_3\times S^3$ and deformations thereof. We exploit the triality symmetry of the underlying duality group ${\rm SO}(4,4)$ of three-dimensional supergravity in order to construct and relate new…

This is an elementary and self--contained review of twistor theory as a geometric tool for solving non-linear differential equations. Solutions to soliton equations like KdV, Tzitzeica, integrable chiral model, BPS monopole or Sine-Gordon…

We study generalized two-field $\alpha$-attractor models whose rescaled scalar manifold is the triply-punctured sphere endowed with its complete hyperbolic metric, whose underlying complex manifold is the modular curve $Y(2)$. Using an…

A new differentiable sphere theorem is obtained from the view of submanifold geometry. An important scalar is defined by the scalar curvature and the mean curvature of an oriented complete submanifold $M^n$ in a space form $F^{n+p}(c)$ with…

We consider quintessence scalar field cosmology in which the Lagrangian of the scalar field is modified by the Generalized Uncertainty Principle. We show that the perturbation terms which arise from the deformed algebra are equivalent with…

We give a global formulation of the coupling of four-dimensional scalar sigma models to Abelian gauge fields for the generalized situation when the "duality structure" of the Abelian gauge theory is described by a flat symplectic vector…

We show a closed Bach-flat Riemannian manifold with a fixed positive constant scalar curvature has to be locally spherical if its Weyl and traceless Ricci tensors are small in the sense of either $L^\infty$ or $L^{\frac{n}{2}}$-norm.…

Thickenings of a metric space capture local geometric properties of the space. Here we exhibit applications of lower bounding the topology of thickenings of the circle and more generally the sphere. We explain interconnections with the…

The works of Commichau--Grauert and Hirschowitz showed that a formal equivalence between embeddings of a compact complex manifold is convergent, if the embeddings have sufficiently positive normal bundles in a suitable sense. We show that…

In the paper a Riemannian structure on the tangent bundle is defined by using a statistical structure $(g,\nabla)$ on the base manifold. Expressions for various curvatures of the structure are derived. Some rigidity results of the structure…

If Kaluza-Klein ideas were correct as an explanation of Yang-Mills and General Relativity on spacetime, the extra fibre geometry would have to be a sphere of constant size of the order of 10 Planck lengths, hence subject to quantum gravity…

Starting with assumptions both simple and natural from "physical" point of view we present a direct construction of transformations preserving wide class of (anti)commutation relations which describe Euclidean/Minkowski superspace…

For an elliptic surface $q:Y \to \Sigma$, with prescribed singular fibres, Stefan Bauer proved directly via algebraic geometry that the stable bundles over $Y$, whose chern classes are pull backs from $\Sigma$, correspond to the stable…