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Start Over Creator Kolář, Ivan

2. Contact elements on fibered manifolds

Creator:
Kolář, Ivan and Mikulski, Włodzimierz M.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
jet of fibered manifold morphism, contact element, Weil bundle, and natural operator
Language:
English
Description:
For every product preserving bundle functor $T^\mu $ on fibered manifolds, we describe the underlying functor of any order $(r,s,q), s\ge r\le q$. We define the bundle $K_{k,l}^{r,s,q} Y$ of $(k,l)$-dimensional contact elements of the order $(r,s,q)$ on a fibered manifold $Y$ and we characterize its elements geometrically. Then we study the bundle of general contact elements of type $\mu $. We also determine all natural transformations of $K_{k,l}^{r,s,q} Y$ into itself and of $T(K_{k,l}^{r,s,q} Y)$ into itself and we find all natural operators lifting projectable vector fields and horizontal one-forms from $Y$ to $K_{k,l}^{r,s,q} Y$.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. Flow prolongation of some tangent valued forms

Creator:
Cabras, Antonella and Kolář, Ivan
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
semibasic tangent valued $k$-form, Frölicher-Nijenhuis bracket, bundle functor, flow prolongation of vector fields, connection, and curvature
Language:
English
Description:
We study the prolongation of semibasic projectable tangent valued $k$-forms on fibered manifolds with respect to a bundle functor $F$ on local isomorphisms that is based on the flow prolongation of vector fields and uses an auxiliary linear $r$-th order connection on the base manifold, where $r$ is the base order of $F$. We find a general condition under which the Frölicher-Nijenhuis bracket is preserved. Special attention is paid to the curvature of connections. The first order jet functor and the tangent functor are discussed in detail. Next we clarify how this prolongation procedure can be extended to arbitrary projectable tangent valued $k$-forms in the case $F$ is a fiber product preserving bundle functor on the category of fibered manifolds with $m$-dimensional bases and local diffeomorphisms as base maps.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

4. On special types of semiholonomic $3$-jets

Creator:
Kolář, Ivan
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
special type of nonholonomic $r$-jet, nonholonomic $r$-jet category, and classification of semiholonomic $3$-jet
Language:
English
Description:
First we summarize some properties of the nonholonomic $r$-jets from the functorial point of view. In particular, we describe the basic properties of our original concept of nonholonomic $r$-jet category. Then we deduce certain properties of the Weil algebras associated with nonholonomic $r$-jets. Next we describe an algorithm for finding the nonholonomic $r$-jet categories. Finally we classify all special types of semiholonomic $3$-jets.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

6. On the Weilian prolongations of natural bundles

Creator:
Kolář, Ivan
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Weil algebra, Weil functor, natural bundle, and gauge natural bundle
Language:
English
Description:
We characterize Weilian prolongations of natural bundles from the viewpoint of certain recent general results. First we describe the iteration $F(EM)$ of two natural bundles $E$ and $F$. Then we discuss the Weilian prolongation of an arbitrary associated bundle. These two auxiliary results enables us to solve our original problem.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public