Cocalibrated G₂-manifolds with Ricci flat characteristic connection

2013/03/29 by Thomas Friedrich, Friedrich, Thomas
Mathematics · Physics and Astronomy · #53 C 25 #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.1303.7444

openalex publication_date 2013/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Any 7-dimensional cocalibrated G₂-manifold admits a unique connection ∇ with skew symmetric torsion. We study these manifolds under the additional condition that the ∇-Ricci tensor vanishes. In particular, we describe their geometry in case of a maximal number of ∇-parallel vector fields.

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