Differential Geometry and Topology

course: Einstein G2-manifolds with closed fundamental 3-form

speaker: Stefan Ivanov (University of Sofia)

abstract: We give an answer to a question posed recently by R.L. Bryant, namely we show that a compact 7-dimensional manifold equipped with a G2-structure with closed fundamental form is Einstein if and only if the Riemannian holonomy of the induced metric is contained in G2. This could be considered to be a G2 analogue of the Goldberg conjecture in almost Kaehler geometry. The result was generalized by Bryant to closed G2-structures with too tightly pinched Ricci tensor. We extend it in another direction proving that a compact G2-manifold with closed fundamental form and divergence-free Weyl tensor is a G2-manifold with parallel fundamental form. We introduce a second symmetric Ricci-type tensor and show that Einstein conditions applied to the two Ricci tensors on a closed G2-structure again imply that the induced metric has holonomy group contained in G2.

timetable:
Mon 27 Sep, 18:15 - 19:15, Sala Conferenze Centro De Giorgi
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