Flows of Spin(7)-structures
Abstract
Description
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.
12 pages. Based on a talk given at the 10th International Conference on Differential Geometry and its Applications, in honour of the 300th anniversary of the birth of Leonhard Euler, Czech Republic. Version 2: Added one remark and one reference
12 pages. Based on a talk given at the 10th International Conference on Differential Geometry and its Applications, in honour of the 300th anniversary of the birth of Leonhard Euler, Czech Republic. Version 2: Added one remark and one reference