Conformal Quaternionic Contact Curvature and the Local Sphere Theorem
نویسنده
چکیده
Abstract. A curvature-type tensor invariant called quaternionic contact (qc) conformal curvature is defined on a qc manifolds in terms of the curvature and torsion of the Biquard connection. The discovered tensor is similar to the Weyl conformal curvature in Riemannian geometry and to the Chern-Moser invariant in CR geometry. It is shown that a qc manifold is locally qc conformal to the standard flat qc structure on the quaternionic Heisenberg group, or equivalently, to the standard 3-sasakian structure on the sphere if and only if the qc conformal curvature vanishes.
منابع مشابه
Conformal Quaternionic Contact Curvature and the Local Sphere Theorem. La Courbure Conforme D’une Structure De Contact Quaternionienne Et Structures Localment Plates
A tensor invariant is defined on a quaternionic contact manifold in terms of the curvature and torsion of the Biquard connection involving derivatives up to third order of the contact form. This tensor, called quaternionic contact conformal curvature, is similar to the Weyl conformal curvature in Riemannian geometry and to the Chern-Moser tensor in CR geometry. It is shown that a quaternionic c...
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