caa a22 4500 606200622 CHVBK 20210128100944.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s00025-014-0413-3 doi (NATIONALLICENCE)springer-10.1007/s00025-014-0413-3 Complete Hypersurfaces with Two Distinct Principal Curvatures in a Space Form [Elektronische Daten] [José Gomes, Henrique de. Lima, Marco Velásquez] In this paper, we study complete hypersurfaces M n immersed in a space form $${\mathbb{Q}_c^{n+1}}$$ Q c n + 1 , with $${c \in \{-1,0,1\}}$$ c ∈ { - 1 , 0 , 1 } and $${n \geq 2}$$ n ≥ 2 , having two distinct principal curvatures with multiplicity p and n − p. In the case that such a hypersurface M n has constant mean curvature, under a suitable restriction on the traceless part of its second fundamental form, we apply a Simons-type formula jointly with the well known generalized maximum principle of Omori-Yau to show that M n must be either isometric to $${\mathbb{S}^{n - p}(r) \times \mathbb{H}^p(-\sqrt{1 + r^2})}$$ S n - p ( r ) × H p ( - 1 + r 2 ) , when c = −1, $${\mathbb{S}^{n - p}(r) \times \mathbb{R}^p}$$ S n - p ( r ) × R p , when c = 0, or $${\mathbb{S}^{n - p}(r) \times \mathbb{S}^p(\sqrt{1 - r^2})}$$ S n - p ( r ) × S p ( 1 - r 2 ) , when c = 1. Afterwards, we use a Cheng-Yau modified operator in order to obtain a sort of extension of this previous result for the context of linear Weingarten hypersurfaces, that is, hypersurfaces whose mean and scalar curvatures are linearly related. Springer Basel, 2014 Space forms nationallicence mean curvature nationallicence normalized scalar curvature nationallicence isoparametric hypersurfaces nationallicence totally umbilical hypersurfaces nationallicence Gomes José Departamento de Matemática, Universidade Federal do Amanozas, 69.077-070, Manaus, Amazonas, Brazil aut de. Lima Henrique Departamento de Matemática, Universidade Federal de Campina Grande, 58.429-970, Campina Grande, Paraíba, Brazil aut Velásquez Marco Departamento de Matemática, Universidade Federal de Campina Grande, 58.429-970, Campina Grande, Paraíba, Brazil aut Results in Mathematics Springer Basel 67/3-4(2015-06-01), 457-470 1422-6383 67:3-4<457 2015 67 25 https://doi.org/10.1007/s00025-014-0413-3 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00025-014-0413-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Gomes José Departamento de Matemática, Universidade Federal do Amanozas, 69.077-070, Manaus, Amazonas, Brazil aut NATIONALLICENCE 700 1- de. Lima Henrique Departamento de Matemática, Universidade Federal de Campina Grande, 58.429-970, Campina Grande, Paraíba, Brazil aut NATIONALLICENCE 700 1- Velásquez Marco Departamento de Matemática, Universidade Federal de Campina Grande, 58.429-970, Campina Grande, Paraíba, Brazil aut NATIONALLICENCE 773 0- Results in Mathematics Springer Basel 67/3-4(2015-06-01), 457-470 1422-6383 67:3-4<457 2015 67 25