arXiv subjects

Marcela Popescu

Publications and source records attributed to Marcela Popescu.

3 recordsLinked to original sources

arXiv2019

Almost Lie Algebroids and Characteristic Classes

Almost Lie algebroids are generalizations of Lie algebroids, when the Jacobiator is not necessary null. A simple example is given, for which a Lie algebroid bracket or a Courant bundle is not possible for the given anchor, but a natural extension of the bundle and the new anchor allows a Lie algebroid bracket. A cohomology and related characteristic classes of an almost Lie algebroid are also constructed. We prove that these characteristic classes are all pull-backs of the characteristic classes of the base space, as in the case of a Lie algebroid.

math.DG↗

arXiv2013

Foliated vector bundles and riemannian foliations

The purpose of this Note is to prove that each of the following conditions is equivalent to that of the foliation ${\cal F}$ is riemannian: 1) the lifted foliation ${\cal F}^{r}$ on the bundle of $r$-transverse jets is riemannian for an $r\geq 1$; 2) the foliation ${\cal F}_{0}^{r}$ on the slashed ${\cal J}_{0}^{r}$ is riemannian and vertically exact for an $r\geq 1 $; 3) there is a positively admissible transverse lagrangian on ${\cal J}%_{0}^{r}E$, the $r$-transverse slashed jet bundle of a foliated bundle $% E\rightarrow M$, for an $r\geq 1$.

math.DG↗

arXiv2012

Affine Hamiltonians in higher order geometry

Affine hamiltonians are defined in the paper and their study is based especially on the fact that in the hyperregular case they are dual objects of lagrangians defined on affine bundles, by mean of natural Legendre maps. The variational problems for affine hamiltonians and lagrangians of order $k\geq 2$ are studied, relating them to a Hamilton equation. An Ostrogradski type theorem is proved: the Hamilton equation of an affine familtonian $h$ is equivalent with Euler-Lagrange equation of its dual lagrangian $L$. Zermelo condition is also studied and some non-trivial examples are given.

math-ph↗