2007/02/28 by Richard Cleyton, Stefan Ivanov
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Curvature #Geometric Analysis and Curvature Flows #Geometry #Holonomy #Manifold (fluid mechanics) #Mathematical analysis #Mathematics #Pure mathematics #Ricci curvature #Ricci decomposition #Riemann curvature tensor #Scalar curvature #Weyl tensor #math-ph #math.DG #math.MP #msc:53C10 #msc:53C25 #msc:53C29
paper · pdf · doi:10.1016/j.geomphys.2008.06.002
LaTeX 2e, 26 pages, 2 tables. Changes in version 2: shortened, reorganized, misprints corrected, several remarks and new introduction. A formula in the proof of Theorem 1.2a has been corrected. Submitted
arxiv created 2007/10/10 · openalex publication_date 2008/06/09 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Explicit formulas for the G2-components of the Riemannian curvature tensor on a manifold with a G2 structure are given in terms of Ricci contractions. We define a conformally invariant Ricci-type tensor that determines the 27-dimensional part of the Weyl tensor and show that its vanishing on compact G2 manifold with closed fundamental form forces the three-form to be parallel. A topological obstruction for the existence of a G2 structure with closed fundamental form is obtained in terms of the integral norms of the curvature components. We produce integral inequalities for closed G2 manifold and investigate limiting cases. We make a study of warped products and cohomogeneity-one G2 manifolds. As a consequence every Fernández-Gray type of G2 structure whose scalar curvature vanishes may be realized such that the metric has holonomy contained in G2.