Publication Date:
2018-03-06
Description:
Associative submanifolds A in nearly parallel G 2 -manifolds Y are minimal 3-submanifolds in spin 7-manifolds with a real Killing spinor. The Riemannian cone over Y has the holonomy group contained in Spin(7) and the Riemannian cone over A is a Cayley submanifold.Infinitesimal deformations of associative submanifolds were considered by the author. This paper is a continuation of the work. We give a necessary and sufficient condition for an infinitesimal associative deformation to be integrable (unobstructed) to second order explicitly. As an application, we show that the infinitesimal deformations of a homogeneous associative submanifold in the 7-sphere given by Lotay, which he called A 3 , are unobstructed to second order.
Print ISSN:
0033-5606
Electronic ISSN:
1464-3847
Topics:
Mathematics
