Flows of Spin(7)-structures

Details Flows of Spin(7)-structures Flows of Spin(7)-structures

2007-09-28

arxiv.org/abs/0709.4594v2

Proceedings of the 10th Conference on Differential Geometry and its Applications: DGA 2007; World Scientific Publishing, (2008

Mathematics

Differential Geometry

12 pages. Based on a talk given at the 10th International Conference on Differential Geometry and its Applications, in honour

Scientific paper

10.1142/9789812790613_0023

We consider flows of Spin(7)-structures. We use local coordinates to describe the torsion tensor of a Spin(7)-structure and derive the evolution equations for a general flow of a Spin(7)-structure on an 8-manifold M. Specifically, we compute the evolution of the metric and the torsion tensor. We also give an explicit description of the decomposition of the space of forms on a manifold with Spin(7)-structure, and derive an analogue of the second Bianchi identity in Spin(7)-geometry. This identity yields an explicit formula for the Ricci tensor and part of the Riemann curvature tensor in terms of the torsion.

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