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

Abstract

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.

14 pages, LaTeX; some minor misprints corrected

References in corpus (1)

• Killing spinors in supergravity with 4-fluxes

Cited by in corpus (9)

• A survey on cosymplectic geometry
• Topology of 3-cosymplectic manifolds
• Generalizations of 3-Sasakian manifolds and skew torsion
• 3-quasi-Sasakian manifolds
• Bi-Legendrian manifolds and paracontact geometry
• The geometry of 3-quasi-Sasakian manifolds
• HyperKahler contact Distribution in 3-Sasakain Manifolds
• HyperKahler Contact Distributions
• A Note on 3-quasi-Sasakian Geometry