5 citations · 17 across the 5 of their papers we have counts for
5 papers
Doubling a cube with positive scalar curvature
Haggai Nuchi
In a 2013 paper, Gromov proves that if smooth Riemannian metrics converge to a smooth Riemannian metric uniformly, and have scalar curvature uniformly bounded below…
Deformation and Extension of Fibrations of Spheres by Great Circles
Patricia Cahn, Herman Gluck, Haggai Nuchi
In a 1983 paper with Frank Warner, we proved that the space of all great circle fibrations of the 3-sphere S^3 deformation retracts to the subspace of Hopf fibrations, and so has t…
Hopf fibrations are characterized by being fiberwise homogeneous
Haggai Nuchi
Heinz Hopf's famous fibrations of the 2n+1-sphere by great circles, the 4n+3-sphere by great 3-spheres, and the 15-sphere by great 7-spheres have a number of interesting properties…
A surprising fibration of S3 x S3 by great 3-spheres
Haggai Nuchi
In this paper, we describe a new surprising example of a fibration of the Clifford torus S3 x S3 in the 7-sphere by great 3-spheres, which is fiberwise homogeneous but whose fibers…
Fiberwise homogeneous fibrations of the 3-dimensional space forms by geodesics
Haggai Nuchi
A fibration of a Riemannian manifold is fiberwise homogeneous if there are isometries of the manifold onto itself, taking any given fiber to any other one, and preserving fibers. E…