Related papers: Singular teleparallelism
In this paper we explore algebraic and geometric structures that arise on parallelizable manifolds. Given a parallelizable manifold $\mathbb{L}$, there exists a global trivialization of the tangent bundle, which defines a map…
We develop the noncommutative geometry (bundles, connections etc.) associated to algebras that factorise into two subalgebras. An example is the factorisation of matrices $M_2(\C)=\C\Z_2\cdot\C\Z_2$. We also further extend the coalgebra…
In this Letter we consider a general quadratic parity-preserving theory for a general flat connection. Imposing a local symmetry under the general linear group singles out the general teleparallel equivalent of General Relativity carrying…
We generalize the concept of affine locally symmetric spaces for parabolic geometries. We discuss mainly $|1|$--graded geometries and we show some restrictions on their curvature coming from the existence of symmetries. We use the theory of…
We survey some aspects of the theory of noncommutative manifolds focusing on the noncommutative analogs of two-dimensional tori and low-dimensional spheres. We are particularly interested in those aspects of the theory that link the…
Teleparallel gravity models, in which the curvature and the nonmetricity of spacetime are both set zero, are widely studied in the literature. We work a different teleparallel theory, in which the curvature and the torsion of spacetime are…
A parametric manifold can be viewed as the manifold of orbits of a (regular) foliation of a manifold by means of a family of curves. If the foliation is hypersurface orthogonal, the parametric manifold is equivalent to the 1-parameter…
A model is presented that could lead to an interesting extension of the Standard Model. Like a supersymmetric gauge theory, the model is holomorphic and invariant to local superspace gauge transformations. However, the model is not…
We review non-linear sigma-models with (2,1) and (2,2) supersymmetry. We focus on off-shell closure of the supersymmetry algebra and give a complete list of (2,2) superfields. We provide evidence to support the conjecture that all N=(2,2)…
Extension of symplectic geometry on manifolds to the supersymmetric case is considered. In the even case it leads to the even symplectic geometry (or, equivalently, to the geometry on supermanifolds endowed with a non-degenerate Poisson…
Following recent work on GLSM localization, we work out curvature couplings for rigidly supersymmetric nonlinear sigma models with superpotential for general target spaces, describing both ordinary and twisted chiral superfields on round…
In this article, we study complete pseudo-Riemannian manifolds whose cone admits a parallel symmetric 2-tensorfield. The situation splits in three cases: nilpotent, decomposable or complex Riemannian. In the complex Riemannian and…
Extended geometry is based on an underlying tensor hierarchy algebra. We extend the previously considered $L_\infty$ structure of the local symmetries (the diffeomorphisms and their reducibility) to incorporate physical fields, field…
I give a brief introduction to and explain the geometry of teleparallel models of modified gravity. In particular I explain why, in my opinion, the covariantised approaches are not needed and the Weitzenb\"ock connection is the most natural…
We show that generalised geometry gives a unified description of maximally supersymmetric consistent truncations of ten- and eleven-dimensional supergravity. In all cases the reduction manifold admits a "generalised parallelisation" with a…
In this article, we focus on symmetric teleparallel gravity, a modification of General Relativity where gravity is described by the non-metricity of an affine connection, whose curvature and torsion vanish. In these theories, the…
Teleparallel theories of gravity are described in terms of the tetrad of a metric and a flat connection with torsion. In this paper, we study spherical symmetry in a modified teleparallel theory of gravity which is based on an arbitrary…
A finite subgroup of the conformal group SL(2,C) can be related to invariant polynomials on a hypersurface in C^3. The latter then carries a simple singularity, which resolves by a finite iteration of basic cycles of deprojections. The…
A theory of cotetrad fields on a four-dimensional manifold is considered. Its configuration space coincides with that of the Teleparallel Equivalent of General Relativity but its dynamics is much simpler. We carry out the Legendre…
Ideas from deformation quantization applied to algebras with one generator lead to methods to treat a nonlinear flat connection. It provides us elements of algebras to be parallel sections. The moduli space of the parallel sections is…