Related papers: Projective vs metric structures

We treat a non-normal Fefferman-type construction based on an inclusion $\SL(n+1)\embed\Spin(n+1,n+1)$. The construction associates a split signature $(n,n)$-conformal spin structure to a projective structure of dimension $n$. For $n\geq 3$…

A diffeological connection on a diffeological vector pseudo-bundle is defined just the usual one on a smooth vector bundle; this is possible to do, because there is a standard diffeological counterpart of the cotangent bundle. On the other…

In this paper, we extend the structure theorem for smooth projective varieties with nef tangent bundle to projective klt varieties whose tangent sheaf is either positively curved or almost nef. Specifically, we show that such a variety $X$,…

A result from Gromov ensures the existence of a contact structure on any connected non-compact odd dimensional Lie group. But in general such structures are not invariant under left translations of the Lie group. The problem of finding…

A Jacobi structure $J$ on a line bundle $L\to M$ is weakly regular if the sharp map $J^\sharp : J^1 L \to DL$ has constant rank. A generalized contact bundle with regular Jacobi structure possess a transverse complex structure. Paralleling…

This paper presents a complete classification of left-invariant affine and projective vector fields on five-dimensional simply connected nilpotent Lie groups endowed with Riemannian metrics. Building on the classification of left-invariant…

Let $C\to M$ be the bundle of connections of a principal bundle on $M$. The solutions to Hamilton-Cartan equations for a gauge-invariant Lagrangian density $\Lambda $ on $C$ satisfying a weak condition of regularity, are shown to admit an…

C-projective structures are analogues of projective structures in the complex setting. The maximal dimension of the Lie algebra of c-projective symmetries of a complex connection on an almost complex manifold of C-dimension $n>1$ is…

We show how to define Riemannian metrics and connections on a noncommutative torus in such a way that an analogue of Levi-Civita's theorem on the existence and uniqueness of a Riemannian connection holds. The major novelty is that we need…

In this paper, firstly we study some left invariant Riemannian metrics on para-hypercomplex 4-dimensional Lie groups. In each Lie group, the Levi-Civita connection and sectional curvature have been given explicitly. We also show these…

This article is concerned with causal structures, which are defined as a field of tangentially non-degenerate projective hypersurfaces in the projectivized tangent bundle of a manifold. The local equivalence problem of causal structures on…

In this paper, left-invariant almost contact metric structures on three-dimensional non-unimodular Lie groups are investigated. It is proved that for every Riemannian Lie group, there is one of these structures. In addition, left-invariant…

We show the correspondence between left invariant flat projective structures on Lie groups and certain prehomogeneous vector spaces. Moreover by using the classification theory of prehomogeneous vector spaces, we classify complex Lie groups…

We study the problem of classifying local projective structures in dimension two having non trivial Lie symmetries. In particular we obtain a classification of flat projective structures having positive dimensional Lie algebra of projective…

The aim of this paper and its sequel is to introduce and classify the holonomy algebras of the projective Tractor connection. After a brief historical background, this paper presents and analyses the projective Cartan and Tractor…

For any flag manifold G/T we obtain an explicit expression of its Levi-Civita connection with respect to any invariant Riemannian metric.

We give a unifying description of all inequivalent vector bundles over the 2-dimensional sphere $S^2$ by constructing suitable global projectors $p$ via equivariant maps. Each projector determines the projective module of finite type of…

Let $(N, J)$ be a simply connected $2n$-dimensional nilpotent Lie group endowed with an invariant complex structure. We define a left invariant Riemannian metric on $N$ compatible with $J$ to be minimal, if it minimizes the norm of the…

This paper is devoted to the study of conformal and projective structures, and especially their connections, in the language of 2-frames, or $G$-structures of 2nd-order. While their normal Cartan connections are well-known, we use the…

Projective structures on curves appear naturally in many areas of mathematics, from extrinsic conformal geometry to analysis, where the main problem is to find qualitative information about the solutions of Hill equations. In this paper, we…