Rigidity of minimal isometric immersions of spheres into spheres
A certain minimal isometric immersion from the sphere \(S^3(1)\) to \(S^6(1/4)\), which is not totally geodesic, has been extensively studied by many authors. In this paper, the author studies uniqueness properties of this immersion proving that it is infinitesimally rigid within the class of all degree 6 minimal isometric immersions. It is also proved that it is linearly rigid; linear rigidity for minimal isometric immersions \(f\) of a manifold \(M\) into the sphere \(S^m\) is equivalent to saying that for each linear transformation \(A\) of \(\mathbb{R}^{m+1}\), the composition \(A\circ f\) is an isometric immersion.
scientific article; zbMATH DE number 1268418