Harmonicity and minimality of oriented distributions
Let \(M\) be a Riemannian manifold. The total space \(P\) of the Grassmann bundle of oriented \(k\)-dimensional vector subspaces of \(TM\) naturally inherits a Riemannian metric. The authors consider sections in the Grassmann bundle, i.e. oriented distributions, as maps between the Riemannian manifolds \(M\) and \(P\) and derive conditions under which such a distribution yields a harmonic map or a minimal immersion. They show that the \(3\)-dimensional distribution of \(S^{4m+3}\) tangent to the quternionic Hopf fibration defines a harmonic map and a minimal immersion. These results are extended to more general situations docming from \(3\)-Sasaki and quaternionic geometry.
scientific article; zbMATH DE number 2141377