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

Publicacions Matemàtiques (1997)

- Volume: 41, Issue: 2, page 383-401
- ISSN: 0214-1493

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topCadek, 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 -

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