74 citations · 110 across the 13 of their papers we have counts for
14 papers
Almost formality of manifolds of low dimension
Domenico Fiorenza, Kotaro Kawai, Hông Vân Lê +1
In this paper we introduce the notion of Poincaré DGCAs of Hodge type, which is a subclass of Poincaré DGCAs encompassing the de Rham algebras of closed orientable manifolds. Then…
The Cramér-Rao inequality on singular statistical models I
Jürgen Jost, Hông Vân Lê, Lorenz Schwachhöfer
We introduce the notion of the essential tangent bundle of a parametrized measure model and the notion of reduced Fisher metric on a (possibly singular) 2-integrable measure model.…
Frölicher-Nijenhuis cohomology on - and -manifolds
Kotaro Kawai, Hông Vân Lê, Lorenz Schwachhöfer
In this paper we show that a parallel differential form of even degree on a Riemannian manifold allows to define a natural differential both on and ,…
Frölicher-Nijenhuis bracket and geometry of -and -manifolds
Kotaro Kawai, Hông Vân Lê, Lorenz Schwachhöfer
We extend the characterization of the integrability of an almost complex structure on differentiable manifolds via the vanishing of the Frölicher-Nijenhuis bracket $[J, J] ^{FN…
Parametrized measure models
Nihat Ay, Jürgen Jost, Hông Vân Lê +1
We develope a new and general notion of parametric measure models and statistical models on an arbitrary sample space which does not assume that all measures of the model have…
Lagrangian submanifolds in strictly nearly Kähler 6-manifolds
Hông Vân Lê, Lorenz Schwachhöfer
Lagrangian submanifolds in strict nearly Kähler 6-manifolds are related to special Lagrangian submanifolds in Calabi-Yau 6-manifolds and coassociative cones in -manifolds. We…
Information geometry and sufficient statistics
Nihat Ay, Jürgen Jost, Hông Vân Lê +1
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 s…
Hypercomplex limits of pluricomplex structures and the Euclidean limit of hyperbolic monopoles
Roger Bielawski, Lorenz Schwachhöfer
We discuss the Euclidean limit of hyperbolic SU(2)-monopoles, framed at infinity, from the point of view of pluricomplex geometry. More generally, we discuss the geometry of hyperc…
Extrinsically Immersed Symplectic Symmetric Spaces
Tom Krantz, Lorenz J. Schwachöfer
Let $(V, \Om)$ be a symplectic vector space and let $ϕ: M \ra V$ be a symplectic immersion. We show that is (locally) an extrinsic symplectic symmetric space (e.s.…
Cohomogeneity one disk bundles with normal homogeneous collars
Lorenz J. Schwachhoefer, Kristopher Tapp
We consider cohomogeneity one homogeneous disk bundles and adress the question when these admit a nonnegatively curved invariant metric with normal collar, i.e., such that near the…
Addendum to "Classification of irreducible holonomies of torsion-free affine connection"
Sergei Merkulov, Lorenz Schwachhöfer
The real form Spin(6,H) in End(R^{32}) of Spin(12,C) in End(C^{32}) is absolutely irreducible and thus satisfies the algebraic identities (40) and (41). Therefore, it also occurs a…
Classification of irreducible holonomies of torsion-free affine connections
Sergei Merkulov, Lorenz Schwachhöfer
The subgroups of GL(n,R) that act irreducibly on R^n and that can occur as the holonomy of a torsion-free affine connection on an n-manifold are classified, thus completing the wor…
Exotic holonomies $\E_7^{(a)}$
Q. -S. Chi, S. A. Merkulov, L. J. Schwachhöfer
It is proved that the Lie groups $\E_7^{(5)}$ and $\E^{(7)}_7$ represented in and the Lie group $\E_7^{\C}$ represented in occur as holonomies of torsion-free…
Exotic Holonomy on Moduli Spaces of Rational Curves
Quo-Shin Chi, Lorenz J Schwachhöfer
Bryant \cite{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 \cite{Ber}. These con…