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Information geometry provides a geometric approach to families of statistical models. The key geometric structures are the Fisher quadratic form and the Amari-Chentsov tensor. In statistics, the notion of sufficient statistic expresses the criterion for passing from one model to another without loss of information. This leads to the question how the… (More)

By a special symplectic connection we mean a torsion free connection which is either the LeviCivita connection of a Bochner-Kähler metric of arbitrary signature, a Bochner-bi-Lagrangian connection, a connection of Ricci type or a connection with special symplectic holonomy. A manifold or orbifold with such a connection is called special symplectic. We show… (More)

- Q.-S Chi, S A Merkulov, L J Schwachhöfer
- 1996

It is proved that the Lie groups E (5) 7 and E (7) 7 represented in R 56 and the Lie group EC7 represented in R 112 occur as holonomies of torsion-free affine connections. It is also shown that the moduli spaces of torsion-free affine connnections with these holonomies are finite dimensional, and that every such connection has a local symmetry group of… (More)

- Pierre Bieliavsky, Michel Cahen, Simone Gutt, John Rawnsley, Lorenz Schwachhöfer
- 2006

This article is an overview of the results obtained in recent years on symplectic connections. We present what is known about preferred connections (critical points of a variational principle). The class of Ricci-type connections (for which the curvature is entirely determined by the Ricci tensor) is described in detail, as well as its far reaching… (More)

The investigation of manifolds with non-negative sectional curvature is one of the classical fields of study in global Riemannian geometry. While there are few known obstruction for a closed manifold to admit metrics of non-negative sectional curvature, there are relatively few known examples and general construction methods of such manifolds (see [Z] for a… (More)

Given the Euclidean space R2n+2 endowed with a constant symplectic structure and the standard flat connection, and given a polynomial of degree 2 on that space, Baguis and Cahen [1] have defined a reduction procedure which yields a symplectic manifold endowed with a Ricci-type connection. We observe that any symplectic manifold (M,ω) of dimension 2n (n ≥ 2)… (More)

One of the classical problems in differential geometry is the investigation of closed manifolds which admit Riemannian metrics with given lower bounds for the sectional or the Ricci curvature and the study of relations between the existence of such metrics and the topology and geometry of the underlying manifold. Despite many efforts during the past… (More)

We consider cohomogeneity one homogeneous disk bundles and adress the question when these admit a nonnegatively curved1 invariant metric with normal collar, i.e., such that near the boundary the metric is the product of an interval and a normal homogeneous space. If such a bundle is not (the quotient of) a trivial bundle, then we show that its rank has to… (More)

Bryant [Br] proved the existence of torsion free connections with exotic holonomy, i.e. with holonomy that does not occur on the classical list of Berger [Ber]. These connections occur on moduli spaces Y of rational contact curves in a contact threefold W. Therefore, they are naturally contained in the moduli space Z of all rational curves in W. We… (More)