Alencar, Hilário; do Carmo, Manfredo; Fernández, Isabel; Tribuzy, Renato A theorem of H. Hopf and the Cauchy-Riemann inequality. II. (English) Zbl 1157.53349 Bull. Braz. Math. Soc. (N.S.) 38, No. 4, 525-532 (2007). Summary: This is a sequel to [Commun. Anal. Geom. 15, No. 2, 283–298 (2007; Zbl 1134.53031)]. Here the result of the previous paper is extended (see the precise statement in Section 1 of the present paper) to surfaces in three-dimensional homogeneous Riemannian manifolds whose group of isometries has dimension four and the bundle curvature is nonzero, whereas in the previous paper only the case of vanishing bundle curvature was treated. Cited in 1 Document MSC: 53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) 20A10 Metamathematical considerations in group theory Keywords:mean curvature; genus zero surface; Hopf’s quadratic form; Cauchy-Riemann inequality Citations:Zbl 1134.53031 PDFBibTeX XMLCite \textit{H. Alencar} et al., Bull. Braz. Math. Soc. (N.S.) 38, No. 4, 525--532 (2007; Zbl 1157.53349) Full Text: DOI Link