On Sp(2) and Sp(2) · Sp(1) structures in 8-dimensional vector bundles.

Cadek, Martin, and Vanzura, Jirí. "On Sp(2) and Sp(2) · Sp(1) structures in 8-dimensional vector bundles.." Publicacions Matemàtiques 41.2 (1997): 383-401. <http://eudml.org/doc/41319>.

@article{Cadek1997,
abstract = {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.},
author = {Cadek, Martin, Vanzura, Jirí},
journal = {Publicacions Matemàtiques},
keywords = {Fibrados; Variedad cerrada; Cuaterniones; Clases características; -structure; -structure; 8-dimensional vector bundle; hyper-Kähler manifold; quaternion-Kähler manifold; linearly independent sections; Cayley numbers; principle of triality; Stiefel-Whitney class; Pontryagin class; Chern class; Euler class; 8-plane bundle},
language = {eng},
number = {2},
pages = {383-401},
title = {On Sp(2) and Sp(2) · Sp(1) structures in 8-dimensional vector bundles.},
url = {http://eudml.org/doc/41319},
volume = {41},
year = {1997},
}

TY - JOUR
AU - Cadek, Martin
AU - Vanzura, Jirí
TI - On Sp(2) and Sp(2) · Sp(1) structures in 8-dimensional vector bundles.
JO - Publicacions Matemàtiques
PY - 1997
VL - 41
IS - 2
SP - 383
EP - 401
AB - 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.
LA - eng
KW - Fibrados; Variedad cerrada; Cuaterniones; Clases características; -structure; -structure; 8-dimensional vector bundle; hyper-Kähler manifold; quaternion-Kähler manifold; linearly independent sections; Cayley numbers; principle of triality; Stiefel-Whitney class; Pontryagin class; Chern class; Euler class; 8-plane bundle
UR - http://eudml.org/doc/41319
ER -