The G 2 Geometry of 3-Sasaki Structures

Abstract

We initiate a systematic study of the deformation theory of the second Einstein metric g15 respectively the proper nearly G 2 structure φ15 of a 3-Sasaki manifold (M7, g) . We show that infinitesimal Einstein deformations for g15 coincide with infinitesimal G 2 deformations for φ15 . The latter are showed to be parametrised by eigenfunctions of the basic Laplacian of g, with eigenvalue twice the Einstein constant of the 4-dimensional base orbifold, via an explicit differential operator. In terms of this parametrisation we determine those infinitesimal G 2 deformations which are unobstructed to second order. © 2023, Mathematica Josephina, Inc.