Iranian Journal of Mathematical Sciences and Informatics
مجله علوم ریاضی و انفورماتیک
IJMSI
Basic Sciences
http://ijmsi.ir
1
admin
1735-4463
2008-9473
8
10.61186/ijmsi
14
8888
13
en
jalali
1400
1
1
gregorian
2021
4
1
16
1
online
1
fulltext
en
On Contact and Symplectic Lie Algeroids
تخصصي
Special
پژوهشي
Research paper
In this paper, we will study compatible triples on Lie algebroids. Using a suitable decomposition for a Lie algebroid, we construct an integrable generalized distribution on the base manifold. As a result, the symplectic form on the Lie algebroid induces a symplectic form on each integral submanifold of the distribution. The induced Poisson structure on the base manifold can be represented by means of the induced Poisson structures on the integral submanifolds. Moreover, for any compatible triple with invariant metric and admissible almost complex structure, we show that the bracket annihilates on the kernel of the anchor map.
Lie algebroid, Symplectic Lie algebroid, Contact Lie algebroid, Poisson structure
35
53
http://ijmsi.ir/browse.php?a_code=A-10-729-1&slc_lang=en&sid=1
E.
Nazari
e.nazari@modares.ac.ir
10031947532846008767
10031947532846008767
No
Tarbiat Modares University
A.
Heydari
aheydari@modares.ac.ir
10031947532846008768
10031947532846008768
Yes
Tarbiat Modares University