Canadian Mathematical Society
Canadian Mathematical Society
  location:  Publicationsjournals
Search results

Search: All articles in the CJM digital archive with keyword holonomy

  Expand all        Collapse all Results 1 - 1 of 1

1. CJM 2005 (vol 57 pp. 1012)

Karigiannis, Spiro
Deformations of $G_2$ and $\Spin(7)$ Structures
We consider some deformations of $G_2$-structures on $7$-manifolds. We discover a canonical way to deform a $G_2$-structure by a vector field in which the associated metric gets ``twisted'' in some way by the vector cross product. We present a system of partial differential equations for an unknown vector field $w$ whose solution would yield a manifold with holonomy $G_2$. Similarly we consider analogous constructions for $\Spin(7)$-structures on $8$-manifolds. Some of the results carry over directly, while others do not because of the increased complexity of the $\Spin(7)$ case.

Keywords:$G_2 \Spin(7)$, holonomy, metrics, cross product
Categories:53C26, 53C29

© Canadian Mathematical Society, 2017 :