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Date:2019-03-13

Indexed by:Journal Article

Date of Publication:2016-02-01

Journal:TAIWANESE JOURNAL OF MATHEMATICS

Included Journals:SCIE

Volume:20

Issue:1

Page Number:205-226

ISSN:1027-5487

Key Words:Non-negative Gaussian curvature; Parallel mean curvature; Product spaces

Abstract:Let M-n(c) be an n-dimensional space form with constant sectional curvature c. Alencar-do Carmo-Tribuzy [5] classified all parallel mean curvature (ab-brev. PMC) surfaces with non-negative Gaussian curvature K in M-n(c) x R with c < 0. Later on, Fetcu-Rosenberg [28] generalized their results for c not equal 0. However, the classification to PMC surfaces in M-n(c) x R with K equivalent to 0 is still open. In this paper, we give a complete classification to the PMC surfaces in M-n(c) R with K equivalent to 0 whose tangent plane spans the constant angle with factor R.