1 citations · 2 across the 5 of their papers we have counts for
6 papers
Entropy of foliations with leafwise Finsler structure
Ilona Michalik, Szymon M. Walczak
We extend the notion of the geometric entropy of foliation to foliated manifolds equipped with leafwise Finsler structure. We study the relation between the geometric entropy and t…
Dupin cyclides osculating surfaces
Adam Bartoszek, Paweł G. Walczak, Szymon M. Walczak
This article is devoted to the study of cyclides osculating general surfaces. We show that generically, at any point of a surface, one has a one-parameter family of cyclides tangen…
On the geometry of warped foliations
Szymon M. Walczak
We discuss the geometry of warped foliations. After examining the Levi-Civita connection, we describe the formulae for sectional, Ricci and scalar curvatures. In the final part of…
Hausdorff leaf spaces for codim-1 foliations
Szymon M. Walczak
The topology of the Hausdorff leaf spaces (HLS) for a codim-1 foliation is the main topic of this paper. At the beginning, the connection between the Hausdorff leaf space and a war…
Separation theorems for compact Hausdorff foliations
Wojciech Kozłowski, Szymon M. Walczak
We investigate compact Hausdorff foliations on compact Riemannian manifolds in the context of the Gromov-Hausdorff distance theory. We give some sufficient conditions for such foli…
Collapse of unit horizontal bundles equipped with a metric of Cheeger-Gromoll type
Wojciech Kozlowski, Szymon M. Walczak
We study unit horizontal bundles associated with Riemannian submersions. First we investigate metric properties of an arbitrary unit horizontal bundle equipped with a Riemannian me…