Manifolds with vectorial torsion

• Published in: Differential geometry and its applications Vol. 45; pp. 130 - 147
• Main Authors: Agricola, Ilka, Kraus, Margarita
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.04.2016
• Subjects: Construction; Curvature; Dirac operator; Equivalence; Fields (mathematics); Joints; Killing spinor; Manifolds; Mathematical analysis; Metric connection with vectorial torsion; Parallel spinor; Torsion; Warped product; Weyl manifold; secondary; Warped product; Killing spinor; Parallel spinor; Weyl manifold; Metric connection with vectorial torsion; Dirac operator; primary

The present note deals with the properties of metric connections ∇ with vectorial torsion V on semi-Riemannian manifolds (Mn,g). We show that the ∇-curvature is symmetric if and only if V♭ is closed, and that V⊥ then defines an (n−1)-dimensional integrable distribution on Mn. If the vector field V i...