arXiv subjects

Robert A. Wolak

Publications and source records attributed to Robert A. Wolak.

3 recordsLinked to original sources

arXiv2026

Cohomology of Quaternionic Foliations and Orbifolds

Starting with a concise review of quaternionic geometry and quaternionic K{ä}hler manifolds, we define a transversely quaternionic K{ä}hler foliation. Then we formulate and prove the foliated versions of the now classical results of V.Y. Kraines and A. Fujiki on the cohomology of quaternionic K{ä}hler manifolds. Finally, as any orbifold can be realized as the leaf space of a suitably defined Riemannian foliation we reformulate our results for quaternionic orbifolds.

math.DG↗

arXiv2021

Twistor spaces on foliated manifolds

The theory of twistors on foliated manifolds is developed and the twistor space of the normal bundle is constructed. It is demonstrated that the classical constructions of the twistor theory lead to foliated objects and permit to formulate and prove foliated versions of some well-known results on holomorphic mappings. Since any orbifold can be understood as the leaf space of a suitable defined Riemannian foliation we obtain orbifold versions of the classical results as a simple consequence of the results on foliated mappings.

math.DG↗

arXiv2015

Transversely Hessian foliations and information geometry

A family of probability distributions parametrized by an open domain $Λ$ in $R^n$ defines the Fisher information matrix on this domain which is positive semi-definite. In information geometry the standard assumption has been that the Fisher information matrix tensor is positive definite defining in this way a Riemannian metric on $Λ$. If we replace the "positive definite" assumption by the existence of a suitable torsion-free connection, a foliation with a transversely Hessian structure appears naturally. In the paper we develop the study of transversely Hessian foliations in view of applications in information geometry.

math.DG↗