Local isometric embeddings of surfaces into a 3-space. (English) Zbl 0967.53039

Ding, Qing; Zhang, Yongqian

Chin. Ann. Math., Ser. B 20, No. 2, 215-222 (1999).

The aim of this paper is to prove that any abstract smooth surface can be locally isometrically embedded into a class of 3-dimensional spaces \(N_{\rho_0}\), parametered by \(\rho_0 >0\), with sectional curvature \(K_{N_{\rho_0}}\) satisfying \(-{1\over \rho^2_0}\leq K_{N_{\rho_0}} \leq 0\).

Reviewer: A.Neagu (Iaşi)

MSC:

53C40	Global submanifolds
53C20	Global Riemannian geometry, including pinching

Keywords:

local isometric embedding; Riemannian manifold; Gauss curvature; sectional curvature