DEFORMATIONS OF NEARLY PARALLEL G(2)-STRUCTURES

作者：Alexandrov Bogdan^*; Semmelmann Uwe

来源：Asian Journal of Mathematics, 2012, 16(4): 713-744.

DOI：10.4310/ajm.2012.v16.n4.a6

• Nearly parallel G(2)-structures
• deformations

We study the infinitesimal deformations of a proper nearly parallel G(2)-structure and prove that they are characterized by a certain first order differential equation. In particular we show that the space of infinitesimal deformations modulo the group of diffeomorphisms is isomorphic to a subspace of co-closed A(27)(3)-eigenforms of the Laplace operator for the eigenvalue 8scal/21. We give a similar description for the space of infinitesimal Einstein deformations of a fixed nearly parallel G(2)-structure. Moreover we show that there are no deformations on the squashed S-7 and on SO(5)/SO(3), but that there are infinitesimal deformations on the Aloff-Wallach manifold N(1, 1) = SU(3)/U(1).

• 出版日期2012-12