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1

Sasakian structures a foliated approach

Wolak R. A.

Demonstratio Mathematica

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2017

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Vol. 50, nr 1

72--82

EN

Recent renewed interest in Sasakian manifolds is due mainly to the fact that they can provide examples of generalized Einstein manifolds, manifolds which are of great interest in mathematical models of various aspects of physical phenomena. Sasakian manifolds are odd dimensional counterparts of Kählerian manifolds to which they are closely related. The paper presents a foliated approach to Sasakian manifolds on which the author gave several lectures. The paper concentrates on cohomological properties of Sasakian manifolds and of transversely holomorphic and Kählerian foliations. These properties permit to formulate obstructions to the existence of Sasakian structures on compact manifolds.

2

Module of a geodesic foliation on the flat torus

Kaźmierczak A.

Journal of Applied Mathematics and Computational Mechanics

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2014

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Vol. 13, nr 4

61--72

EN

We study properties of geodesic foliations on the flat, n-dimensional torus. Using the isomorphism of the Hodge star, we obtain some facts concerning compact totally geodesic surfaces (which are the leaves of geodesic foliations). We compute the p-module of a geodesic foliation. On the basis of these results, we derive a kind of reciprocity formula for the product of modules of two orthogonal foliations. We relate this product with the number of intersections of their leaves. We also obtain a formula for a product of modules of a finite number of geodesic foliations.

3

Examples of non-conformal submersions from spheres with umbilical fibers

Zawadzki T.

Demonstratio Mathematica

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2014

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Vol. 47, nr 3

738--747

EN

We directly prove that the foliation of the sphere S2n+1, the leaves of which are intersections of all complex linear 2-dimensional subspaces of Cn+1 translated by a constant vector p, defines a submersion that is horizontally conformal if and only if p = 0. We generalise this result to the cases of S4n+3 and S15 with foliations constructed using quaternionic and octonionic structure (resp.) in an analogous way.

4

Deformation structures in the gneissic exotic pebbles from the area of Wołosate (Cisna sandstone, Dukla tectonic unit, Outer Carpathians, Poland)

Kania M., Wolska A.

Annales Societatis Geologorum Poloniae

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2009

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Vol. 79, No 1

41-52

EN

Gneissic exotic pebbles from the Cisna beds (Dukla tectonic unit) in the region of Wołosate (Bieszczady Mts., Eastern Carpathians) were investigated. These exotic pebbles are from 9.5 to 13 cm in size. Basing on the structural features, the following groups of exotic pebbles were distinguished: granitic gneisses, laminated gneisses, flaser gneisses and mylonitic gneisses. Granite - granodiorite protolith was deformed in the shear zone; strain partitioning was probably an important process during deformation. The observed structures allow to determine the temperature of metamorphism as 500-550°C. The lower limit of pressure was determined basing on phengite geobarometer as 5 kbar. The nature and localization of the source area can be similar to the Bretila sequence from the Romanian Eastern Carpathians.

5

On the perfectness of C∞ s-diffeomorphism groups on a foliated manifold

Lech J.

Opuscula Mathematica

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2008

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Vol. 28, no. 3

313-324

EN

The notion of Cr,s and C∞,s-diffeomorphisms is introduced. It is shown that the identity component of the group of leaf preserving C∞,s-diffeomorphisms with compact supports is perfect. This result is a modification of the Mather and Epstein perfectness theorem.

6

A modulus and an extremal form of a foliation

Blachowska D.

Demonstratio Mathematica

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2004

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Vol. 37, nr 4

939--954

EN

We prove that the p-modulus of the foliation is conformal invariant. We study the problem of existing of the extremal form for a foliaton on Riemannian manifold. We also compute the value of p-modulus and the extremal form for k-dimensional foliation given by a submersion.

7

Morphostructural zones of the Myrdalsjokull ice cap and its main outlet glacier the Hofdabrekkujokull, Iceland

Olszewski A., Weckwerth P.

Landform Analysis

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1999

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Vol. 2

51--62

EN

The problem of the morphostructures of glaciers is directly associated, certainly as far as its condition and origin is concerned, with topographical, geomorphological and geological rock foundations, surrounding those at the bedrock of glaciers and also, in case of valley and outflow glaciers, with those of the valley slopes. differentiation of the bedrock of the Myrdalsjokull ice cap leads to a classification of its three morphostructural zones: the glaciomorphological centre (A) which has only slightly varied relief (a,- a4), a northern homogeneous macro-cone of radial flow (B), and a bipartite, supramarginal surrounding slope (C), which has a significant development of outflow glaciers. This differentiation of the subglacial relief and the rocky surrounding of the Hofdabrekkujokull, are manifested in the distribution of various types of foliation and fissuring on its subaerial surface. These, together with its hypsometric formation, were the basis for distinguishing four morphostructural zones of this glacier (Ht - H4). The distinctive morphostructural features of the sector of the bottom zone (H4) of the glacier determine the areas of its particular activity; this reflects the lithogenetic and morphogenetic nature of the subglacial bedrock. The deformed deposits of the bedrock and the nearest forefield represent an important dynamic effect of the glacial system.