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Displaying similar documents to “Note on a generalization of the generalized vector field problem”

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

Martin Cadek, Jirí Vanzura (1997)

Publicacions Matemàtiques

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Let ξ be an oriented 8-dimensional vector bundle. We prove that the structure group SO(8) of ξ can be reduced to S(2) or S(2) · S(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 S(2)- structure in ξ over a closed connected spin manifold of dimension 8 are also given in terms of characteristic classes. ...

On sectioning tangent bundles and other vector bundles

Korbaš, Július, Zvengrowski, Peter

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This paper has two parts. Part one is mainly intended as a general introduction to the problem of sectioning vector bundles (in particular tangent bundles of smooth manifolds) by everywhere linearly independent sections, giving a survey of some ideas, methods and results.Part two then records some recent progress in sectioning tangent bundles of several families of specific manifolds.