We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Contactomorphisms and Lychagin 1-form.
- Authors
Luganda, Fidele Balibuno; Landa, Alain Musesa
- Abstract
In [5], Lychagin constructed a smooth chart from the group of contactomorphisms. From this chart, Lychagin showed that the connected component of the identity of the group of contactomorphism is arc wise connected. In [2], it has been shown that the contactomorphism group enjoys the fragmentation property. Herein, we introduce the Lychagin 1-form and the relation between the contactomorphism and the Lychagin 1-form defined on the 1-jet bundle. By the way, we characterize the contact diffeomorphisms by means of the closedness of the Lychagin 1-form. This characterization is known by geometers long time ago through the joint work of Sniatyki and Tulczjew [8]. We give the same characterization in this paper using the geometry of Legendre submanifolds through the Lychagin chart. This last result is the analogue of the Sniatyki-Tulczjew characterization of symplectomorphisms in contact geometry[1].
- Subjects
GROUP identity; SUBMANIFOLDS; DIFFEOMORPHISMS; GEOMETRY
- Publication
Balkan Journal of Geometry & Its Applications, 2022, Vol 27, Issue 1, p11
- ISSN
1224-2780
- Publication type
Article