One-to-one projectability of closed surfaces in a spherical space (Q650389)

There is well known conjecture that every compact regular surface \(F\) of Gaussian curvature \(k > 0\) in the spherical space \(S^3\) is projected one-to-one onto a great totally geodesic sphere \(S^2_0\). In this paper, it is proven, under some restriction on the normal curvature of \(F\), that, if \(F\) is a compact \(C^2\) surface in the spherical space \(S^3\), then \(F\) is projected one-to-one onto a great sphere.