Abstract
The tangent bundle to the n-dimensional sphere is the space of oriented lines in \(\mathbb{R}^{n+1}\). We characterise the smooth sections of \(T S^{n}\rightarrow S^{n}\) which correspond to points in \(\mathbb{R}^{n+1}\) as gradients of eigenfunctions of the Laplacian on Sn with eigenvalue n. The special case of n=6 and its connection with almost complex geometry is discussed.
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