Abstract
The squashed 7-sphere $S^{7}$ is a 7-sphere with an Einstein metric given by the canonical variation and its cone $\mathbb{R}^{8} - \{ 0 \}$ has full holonomy ${\rm Spin}(7)$. There is a canonical calibrating 4-form $\Phi$ on $\mathbb{R}^{8} - \{ 0 \}$. A minimal 3-submanifold in $S^{7}$ is called associative if its cone is calibrated by $\Phi$. In this paper, we classify two types of fundamental associative submanifolds in the squashed $S^{7}$. One is obtained by the intersection with a 4-plane and the other is homogeneous. Then we study their infinitesimal associative deformations and explicitly show that all of them are integrable.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Similar Papers
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.