A theorem of H.!Hopf and the Cauchy-Riemann inequality II

被引：3

作者：

Alencar, Hilario ^{[1
]}

Do Carmo, Manfredo ^{[2
]}

Fernandez, Isabel ^{[3
]}

Tribuzy, Renato ^{[4
]}

机构：

[1] Univ Fed Alagoas, Inst Matemat, BR-57072900 Maceio, AL, Brazil

[2] IMPA, BR-22460320 Rio De Janeiro, Brazil

[3] Univ Seville, Dept Matemat Aplicada 1, ETS Ingn Informat, E-41012 Seville, Spain

[4] Univ Fed Amazonas, Inst Ciencias Exatas, Dept Matemat, BR-69077000 Manaus, Amazonas, Brazil

来源：

BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY | 2007年 / 38卷 / 04期

关键词：

mean curvature; genus zero surface; Hopf's quadratic form; Cauchy-Riemann inequality;

D O I：

10.1007/s00574-007-0058-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This is a sequel to "A theorem of H. Hopf and the Cauchy-Riemann inequality" [AdCT]. 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.

引用

页码：525 / 532

页数：8

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