Cayley fibrations in the Bryant-Salamon $Spin(7)$ manifold

DOI10.1007/S10231-022-01273-ZarXiv2110.09433MaRDI QIDQ6380678

Publication date: 18 October 2021

Abstract: On each complete asymptotically conical

S p i n (7)

manifold constructed by Bryant and Salamon, including the asymptotic cones, we consider a natural family of

S U (2)

actions preserving the Cayley form. For each element of this family, we study the (possibly singular) invariant Cayley fibration, which we describe explicitly, if possible. These can be reckoned as generalizations of the trivial flat fibration of

m a t h b b R^{8}

and the product of a line with the Harvey-Lawson coassociative fibration of

m a t h b b R^{7}

. The fibres will provide new examples of asymptotically conical Cayley submanifolds in the Bryant-Salamon manifolds of topology

m a t h b b R^{4}, m a t h b b R i m e s S^{3}

and

m a t h c a l O_{C P^{1}} (- 1)

.

Mathematics Subject Classification ID

Twistor theory, double fibrations (complex-analytic aspects) (32L25) Spin and Spin({}^c) geometry (53C27) Global submanifolds (53C40) Issues of holonomy in differential geometry (53C29) Calibrations and calibrated geometries (53C38)

This page was built for publication: Cayley fibrations in the Bryant-Salamon $Spin(7)$ manifold

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6380678)