On riemannian manifolds admitting a function whose gradient is of constant norm ii

Abstract

We continue to study the metrical structure of complete Riemannian manifolds which admit a smooth function f with ‖∇f‖ ≡ 1 for the gradient vector ∇f. We again show that Ricci curvatures controll such metric structure considerably appealing to recent Cheeger-Colding's methods. © 1998, Department of Mathematics, Tokyo Institute of Technology. All rights reserved.