caa a22 4500 445836202 CHVBK 20180317145331.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s00209-009-0633-5 doi (NATIONALLICENCE)springer-10.1007/s00209-009-0633-5 The Gauss-Kronecker curvature of minimal hypersurfaces in four-dimensional space forms [Elektronische Daten] [A. Asperti, R. Chaves, L. Sousa Jr.] Let $${{\mathbb{Q}^4}(c)}$$ be a four-dimensional space form of constant curvature c. In this paper we show that the infimum of the absolute value of the Gauss-Kronecker curvature of a complete minimal hypersurface in $${\mathbb{Q}^4(c), c\leq 0}$$, whose Ricci curvature is bounded from below, is equal to zero. Further, we study the connected minimal hypersurfaces M 3 of a space form $${{\mathbb{Q}^4}(c)}$$ with constant Gauss-Kronecker curvature K. For the case c ≤ 0, we prove, by a local argument, that if K is constant, then K must be equal to zero. We also present a classification of complete minimal hypersurfaces of $${\mathbb{Q}^4(c)}$$ with K constant. Springer-Verlag, 2009 Minimal hypersurfaces in space forms nationallicence Gauss-Kronecker curvature nationallicence Asperti A. Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão, 1010, CEP 05508-090, São Paulo, SP, Brazil aut Chaves R. Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão, 1010, CEP 05508-090, São Paulo, SP, Brazil aut Sousa Jr. L. Departamento de Matemática e Estatística, Universidade Federal do Estado do Rio de Janeiro, Avenida Pasteur, 458, Urca, CEP 22290-240, Rio de Janeiro, RJ, Brazil aut Mathematische Zeitschrift Springer-Verlag 267/3-4(2011-04-01), 523-533 0025-5874 267:3-4<523 2011 267 209 https://doi.org/10.1007/s00209-009-0633-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-009-0633-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Asperti A. Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão, 1010, CEP 05508-090, São Paulo, SP, Brazil aut NATIONALLICENCE 700 1- Chaves R. Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão, 1010, CEP 05508-090, São Paulo, SP, Brazil aut NATIONALLICENCE 700 1- Sousa Jr L. Departamento de Matemática e Estatística, Universidade Federal do Estado do Rio de Janeiro, Avenida Pasteur, 458, Urca, CEP 22290-240, Rio de Janeiro, RJ, Brazil aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 267/3-4(2011-04-01), 523-533 0025-5874 267:3-4<523 2011 267 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer