Related papers: Holonomy and four-dimensional manifolds

Four dimensional simply connected Lie groups admitting a pseudo K\"ahler metric are determined. The corresponding Lie algebras are modelized and the compatible pairs $(J,\omega)$ are parametrized up to complex isomorphism (where $J$ is a…

A conformal transformation of a semi-Riemannian manifold is essential if there is no conformally equivalent metric for which it is an isometry. For Riemannian manifolds the existence of an essential conformal transformation forces the…

We develop a general structure theory for compact homogeneous Riemannian manifolds in relation to the co-index of symmetry. We will then use these results to classify irreducible, simply connected, compact homogeneous Riemannian manifolds…

In this paper we establish a one-to-one correspondence between $S^1$-gerbes with connections, on the one hand, and their holonomies, for simply connected manifolds, or their parallel transports, in the general case, on the other hand. This…

Let X be a closed manifold of dimension 2m >= 6 with torsion-free middle-dimensional homology. We construct metrics on X of arbitrarily small volume, such that every middle-dimensional submanifold of less than unit volume necessarily…

This article is concerned with the study of the holonomy group of flat solvmanifolds. It is known that the holonomy group of a flat solvmanifold is abelian; we give an elementary proof of this fact and moreover we prove that any finite…

We study the normal holonomy group, i.e. the holonomy group of the normal connection, of a CR-submanifold of a complex space form. We complete the local classification of normal holonomies for complex submanifolds. We show that the normal…

In this paper, we investigate the holonomy group of $n$-dimensional projective Finsler metrics of constant curvature. We establish that in the spherically symmetric case, the holonomy group is maximal, and for a simply connected manifold it…

Normal distribution manifolds play essential roles in the theory of information geometry, so do holonomy groups in classification of Riemannian manifolds. After some necessary preliminaries on information geometry and holonomy groups, it is…

We consider two Riemannian geometries for the manifold $\mathcal{M}(p,m\times n)$ of all $m\times n$ matrices of rank $p$. The geometries are induced on $\mathcal{M}(p,m\times n)$ by viewing it as the base manifold of the submersion…

In a joint work with Saji, the second and the third authors gave an intrinsic formulation of wave fronts and proved a realization theorem of wave fronts in space forms. As an application, we show that the following four objects are…

In this paper we demonstrate how sub-Riemannian geometry can be used for manifold learning and surface reconstruction by combining local linear approximations of a point cloud to obtain lower dimensional bundles. Local approximations…

For every $k \geq 2$ and $n \geq 2$ we construct $n$ pairwise homotopically inequivalent simply-connected, closed $4k$-dimensional manifolds, all of which are stably diffeomorphic to one another. Each of these manifolds has hyperbolic…

A self-dual harmonic 2-form on a 4-dimensional Riemannian manifold is symplectic where it does not vanish. Furthermore, away from the form's zero set, the metric with the 2-form give a compatible almost complex structure and thus…

We study homogeneous Lorentzian manifolds $M = G/L$ of a connected reductive Lie group $G$ modulo a connected reductive subgroup $L$, under the assumption that $M$ is (almost) $G$-effective and the isotropy representation is totally…

Hiss and Szczepa\'nski proved in 1991 that the holonomy group of any compact flat Riemannian manifold, of dimension at least two, acts reducibly on the rational span of the Euclidean lattice associated with the manifold via the first…

We study almost Hermitian 4-manifolds with holonomy algebra, for the canonical Hermitian connection, of dimension at most one. We show how Riemannian 4-manifolds admitting five orthonormal symplectic forms fit therein and classify them. In…

Every open manifold L of dimension greater than one has complete Riemannian metrics g with bounded geometry such that (L,g) is not quasi-isometric to a leaf of a codimension one foliation of a closed manifold. Hence no conditions on the…

We study the manifold of all Riemannian metrics over a closed, finite-dimensional manifold. In particular, we investigate the topology on the manifold of metrics induced by the distance function of the L^2 Riemannian metric - so called…

We study the isometry groups and Killing vector fields of a family of pseudo-Riemannian metrics on Euclidean space which have neutral signature (3+2p,3+2p). All are p+2 curvature homogeneous, all have vanishing Weyl scalar invariants, all…