Holonomy and 3-Sasakian homogeneous manifolds versus symplectic triple systems
Differential Geometry
2019-03-20 v1
Abstract
Our aim is to support the choice of two remarkable connections with torsion in a 3-Sasakian manifold, proving that, in contrast to the Levi-Civita connection, the holonomy group in the homogeneous cases reduces to a proper subgroup of the special orthogonal group, of dimension considerably smaller. We realize the computations of the holonomies in a unified way, by using as a main algebraic tool a nonassociative structure, that one of symplectic triple system.
Keywords
Cite
@article{arxiv.1903.07815,
title = {Holonomy and 3-Sasakian homogeneous manifolds versus symplectic triple systems},
author = {Cristina Draper},
journal= {arXiv preprint arXiv:1903.07815},
year = {2019}
}
Comments
21 pages