Related papers: A note on flat metric connections with antisymmetr…
We show a correspondence between the set of all G-invariant projectively flat connections on a homogeneous apace $M=G/K$, and the one of all {G}^~-invariant flat connections on a homogeneous space {M}^~={G}^~/K, where {G}^~ is a central…
We study connections on hermitian modules, and show that metric connections exist on regular hermitian modules; i.e finitely generated projective modules together with a non-singular hermitian form. In addition, we develop an index calculus…
In a talk at the conference {\it Geometrical Foundations of Gravity at Tartu 2017}, it was suggested that the affine spacetime connection could be associated with purely fictitious forces. This leads to gravitation in a flat and smooth…
In 1983, Conway-Gordon showed that for every spatial complete graph on 6 vertices, the sum of the linking numbers over all of the constituent 2-component links is congruent to 1 modulo 2, and for every spatial complete graph on 7 vertices,…
We define a non-commutative version of the $A_1$ T-system, which underlies frieze patterns of the integer plane. This system has discrete conserved quantities and has a particular reduction to the known non-commutative Q-system for $A_1$.…
We study the types of non-integrable $\mathrm{G}$-structures on Riemannian manifolds. In particular, geometric types admitting a connection with totally skew-symmetric torsion are characterized. 8-dimensional manifolds equipped with a…
We study lattices in non-positively curved metric spaces. Borel density is established in that setting as well as a form of Mostow rigidity. A converse to the flat torus theorem is provided. Geometric arithmeticity results are obtained…
Witten and Yau (hep-th/9910245) have recently considered a generalisation of the AdS/CFT correspondence, and have shown that the relevant manifolds have certain physically desirable properties when the scalar curvature of the boundary is…
Based on a general formula due to R.Bryant, we work out the topological structure of the space of torsion-free $G_2$-structures generating the same associated Riemannian metric on a compact $7$-manifold. We also identify a corresponding Lie…
We complete the classification of compact Hermitian manifolds admitting a flat Gauduchon connection. In particular, we establish a conjecture of Yang and Zheng, showing that apart from the cases of a flat Chern or Bismut connection, such…
A holomorphic 1-form on a compact Riemann surface S naturally defines a flat metric on S with cone-type singularities. We present the following surprising phenomenon: having found a geodesic segment (saddle connection) joining a pair of…
We compute the homotopy type of the moduli space of flat, unitary connections over aspherical surfaces, after stabilizing with respect to the rank of the underlying bundle. Over the orientable surface M^g, we show that this space has the…
In 1995, S. Adams and G. Stuck as well as A. Zeghib independently provided a classification of non-compact Lie groups which can act isometrically and locally effectively on compact Lorentzian manifolds. In the case that the corresponding…
Connections compatible with degenerate metric structures are known to possess peculiar features: on the one hand, the compatibility conditions involve restrictions on the torsion; on the other hand, torsionfree compatible connections are…
We construct examples of compact homogeneous Riemannian manifolds admitting an invariant Bismut connection that is Ricci flat and non-flat, proving in this way that the generalized Alekseevsky-Kimelfeld theorem does not hold. The…
Hypertranslations and hyperrotations are asymptotic symmetries of flat space, on top of the familiar supertranslations and superrotations. They were discovered in arXiv:2205.01422 by working in the Special Double Null (SDN) gauge, where…
In arXiv:math/0105152, the second author used the Kontsevich deformation quantization technique to define a natural connection \omega_n on the compactified configuration spaces of n points on the upper half-plane. This connection takes…
We give a full classification of general affine connections on Galilei manifolds in terms of independently specifiable tensor fields. This generalises the well-known case of (torsional) Galilei connections, i.e. connections compatible with…
For a commutative ring $R$ with unit $1\ne 0$ and a multiplicatively closed subset $S$ of $R$, we introduce a new topology on the $S$-prime spectrum $\mathrm{Spec}_SR$ of $R$ called the $S$-flat topology. Our aims is to give an algebraic…
In this paper, a Riemannian geometry of noncommutative super surfaces is developed which generalizes [4] to the super case. The notions of metric and connections on such noncommutative super surfaces are introduced and it is shown that the…