Let ξ be an oriented 8-dimensional vector bundle. We prove that the structure group SO(8) of ξ can be reduced to Sp(2) or Sp(2) · Sp(1) if and only if the vector bundle associated to ξ via a certain outer automorphism of the group Spin(8) has 3 linearly independent sections or contains a 3-dimensional subbundle. Necessary and sufficient conditions for the existence of an Sp(2)- structure in ξ over a closed connected spin manifold of dimension 8 are also given in terms of characteristic classes.
@article{urn:eudml:doc:41319,
title = {On Sp(2) and Sp(2) $\cdot$ Sp(1) structures in 8-dimensional vector bundles.},
journal = {Publicacions Matem\`atiques},
volume = {41},
year = {1997},
pages = {383-401},
mrnumber = {MR1485490},
zbl = {0896.57015},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41319}
}
Cadek, Martin; Vanzura, Jirí. On Sp(2) and Sp(2) · Sp(1) structures in 8-dimensional vector bundles.. Publicacions Matemàtiques, Tome 41 (1997) pp. 383-401. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41319/