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1
Content available remote

On the first secondary invariant of Molino's central sheaf

100%
Álvarez López J.
Annales Polonici Mathematici
|
1996
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tom 64
|
nr 3
253-265
EN
For a Riemannian foliation on a closed manifold, the first secondary invariant of Molino's central sheaf is an obstruction to tautness. Another obstruction is the class defined by the basic component of the mean curvature with respect to some metric. Both obstructions are proved to be the same up to a constant, and other geometric properties are also proved to be equivalent to tautness.
2
Content available remote

A type of non-equivalent pseudogroups. Application to foliations

80%
Alvarez López J.
Annales Polonici Mathematici
|
1991-1992
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tom 56
|
nr 2
187-194
EN
A topological result for non-Hausdorff spaces is proved and used to obtain a non-equivalence theorem for pseudogroups of local transformations. This theorem is applied to the holonomy pseudogroup of foliations.
3
Content available remote

Jacobi operator for leaf geodesics

80%
Walczak P. G.
Colloquium Mathematicum
|
1993
|
tom 65
|
nr 2
213-226
4
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The graph of a totally geodesic foliation

80%
Wolak R.
Annales Polonici Mathematici
|
1994-1995
|
tom 60
|
nr 3
241-247
EN
We study the properties of the graph of a totally geodesic foliation. We limit our considerations to basic properties of the graph, and from them we derive several interesting corollaries on the structure of leaves.
5
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On extendability of invariant distributions

80%
Ziemian B.
Annales Polonici Mathematici
|
2000
|
tom 74
|
nr 1
13-25
EN
In this paper sufficient conditions are given in order that every distribution invariant under a Lie group extend from the set of orbits of maximal dimension to the whole of the space. It is shown that these conditions are satisfied for the n-point action of the pure Lorentz group and for a standard action of the Lorentz group of arbitrary signature.
6
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Dimension Distortion by Sobolev Mappings in Foliated Metric Spaces

70%
Balogh Z. M., Tyson J. T., Wildrick K.
Analysis and Geometry in Metric Spaces
|
2013
|
tom 1
232-254
EN
We quantify the extent to which a supercritical Sobolev mapping can increase the dimension of subsets of its domain, in the setting of metric measure spaces supporting a Poincaré inequality. We show that the set of mappings that distort the dimensions of sets by the maximum possible amount is a prevalent subset of the relevant function space. For foliations of a metric space X defined by a David–Semmes regular mapping Π : X → W, we quantitatively estimate, in terms of Hausdorff dimension in W, the size of the set of leaves of the foliation that are mapped onto sets of higher dimension. We discuss key examples of such foliations, including foliations of the Heisenberg group by left and right cosets of horizontal subgroups.
7
Content available remote

Harmonic conformal flows on manifolds of constant curvature

51%
Fawaz A.
Open Mathematics
|
2007
|
tom 5
|
nr 3
493-504
EN
We compute the energy of conformal flows on Riemannian manifolds and we prove that conformal flows on manifolds of constant curvature are critical if and only if they are isometric.
8
Content available remote

On the role of partial Ricci curvature in the geometry of submanifolds and foliations

51%
Rovenskiĭ V.
Annales Polonici Mathematici
|
1998
|
tom 68
|
nr 1
61-82
EN
Submanifolds and foliations with restrictions on q-Ricci curvature are studied. In §1 we estimate the distance between two compact submanifolds in a space of positive q-Ricci curvature, and give applications to special classes of submanifolds and foliations: k-saddle, totally geodesic, with nonpositive extrinsic q-Ricci curvature. In §2 we generalize a lemma by T. Otsuki on asymptotic vectors of a bilinear form and then estimate from below the radius of an immersed submanifold in a simply connected Riemannian space with nonpositive curvature; moreover, we prove a theorem on nonembedding into a circular cylinder when the ambient space is Euclidean. Corollaries are nonembedding theorems of Riemannian manifolds with nonpositive q-Ricci curvature into a Euclidean space. In §3 a lower estimate of the index of relative nullity of a submanifold with nonpositive extrinsic q-Ricci curvature is proven. Corollaries are extremal theorems for a compact submanifold with the nullity foliation in a Riemannian space of positive curvature. On the way, some results by T. Frankel, K. Kenmotsu and C. Xia, J. Morvan, A. Borisenko, S. Tanno, B. O'Neill, J. Moore, T. Ishihara, H. Jacobowitz, L. Florit, M. Dajczer and L. Rodríguez are generalized.
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