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- W4250252561 abstract "Each great circle fibration of the unit $3$-sphere in $4$-space can be identified with a subset of the Grassmann manifold of oriented $2$-planes in $4$-space by associating each great circle fiber with the $2$-plane it lies in. This Grassmann manifold can be identified with the space ${S^2} times {S^2}$. H. Gluck and F. Warner, in Great circle fibrations of the three sphere, Duke Math. J. 50 (1983), 107-132, have shown that the subsets of this Grassmann manifold which correspond to great circle fibrations can be interpreted as the graphs of distance decreasing maps from ${S^2}$ and ${S^2}$ and that Hopf fibrations correspond to constant maps. This note characterizes explicitly the maps which correspond to skew-Hopf fibrations: those fibrations of the $3$-sphere obtained from Hopf fibrations by applying a linear transformation of $4$-space followed by projection of the fibers back to the unit $3$-sphere." @default.
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- W4250252561 date "1985-01-01" @default.
- W4250252561 modified "2023-09-30" @default.
- W4250252561 title "A Note on Skew-Hopf Fibrations" @default.
- W4250252561 doi "https://doi.org/10.2307/2044571" @default.
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