3-Sasakian manifolds, 3-cosymplectic manifolds and Darboux theorem

Details 3-Sasakian manifolds, 3-cosymplectic manifolds and Darboux theorem 3-Sasakian manifolds, 3-cosymplectic manifolds and Darboux theorem

2007-03-08

arxiv.org/abs/math/0703219v5

J. Geom. Phys. 57 (2007), no. 12, 2509-2520

Mathematics

Differential Geometry

14 pages, LaTeX; some minor misprints corrected

Scientific paper

10.1016/j.geomphys.2007.09.001

We present a compared analysis of some properties of 3-Sasakian and 3-cosymplectic manifolds. We construct a canonical connection on an almost 3-contact metric manifold which generalises the Tanaka-Webster connection of a contact metric manifold and we use this connection to show that a 3-Sasakian manifold does not admit any Darboux-like coordinate system. Moreover, we prove that any 3-cosymplectic manifold is Ricci-flat and admits a Darboux coordinate system if and only it is flat.

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