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Entropy of distal groups, pseudogroups, foliations and laminations

100%
Biś A., Walczak P.
Annales Polonici Mathematici
|
2011
|
tom 100
|
nr 1
45-54
EN
A distality property for pseudogroups and foliations is defined. Distal foliated bundles satisfying some growth conditions are shown to have zero geometric entropy in the sense of É. Ghys, R. Langevin and P. Walczak [Acta Math. 160 (1988)].
2
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Foliations by surfaces of a peculiar class

100%
Bartoszek A., Walczak P.
Annales Polonici Mathematici
|
2008
|
tom 94
|
nr 1
89-95
EN
We classify surfaces in 3-dimensional space forms which have all the local conformal invariants constant and show that compact 3-manifolds of nonzero constant sectional curvature admit no foliations by such surfaces.
3
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Foliations making a constant angle with principal directions on ellipsoids

81%
Garcia R., Langevin R., Walczak P.
Annales Polonici Mathematici
|
2015
|
tom 113
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nr 2
165-173
EN
We study the global behavior of foliations of ellipsoids by curves making a constant angle with the lines of curvature.
4
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Only one of generalized gradients can be elliptic

81%
Kalina J., Pierzchalski A., Walczak P.
Annales Polonici Mathematici
|
1997
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tom 67
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nr 2
111-120
EN
Decomposing the space of k-tensors on a manifold M into the components invariant and irreducible under the action of GL(n) (or O(n) when M carries a Riemannian structure) one can define generalized gradients as differential operators obtained from a linear connection ∇ on M by restriction and projection to such components. We study the ellipticity of gradients defined in this way.
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