SURFACES WITH CONSTANT MEAN CURVATURE IN RIEMANNIAN PRODUCTS

被引：4

作者：

De Lira, Jorge H. S. ^{[1
]}

Vitorio, Feliciano A. ^{[2
]}

机构：

[1] Univ Fed Ceara, Dept Matemat, BR-60455760 Fortaleza, Ceara, Brazil

[2] Univ Fed Alagoas, Dept Matemat, BR-57072900 Maceio, Alagoas, Brazil

来源：

QUARTERLY JOURNAL OF MATHEMATICS | 2010年 / 61卷 / 01期

关键词：

THEOREM; INEQUALITY; HOPF;

D O I：

10.1093/qmath/han030

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove the existence of holomorphic quadratic differentials for surfaces with parallel mean curvature in some four-dimensional products of space forms. These differentials are then used to characterize spheres with parallel mean curvature immersed into these spaces.

引用

页码：33 / 41

页数：9

共 50 条

[1] Constant mean curvature surfaces in sub-Riemannian geometry
Hladky, Robert K.
Pauls, Scott D.
[J]. JOURNAL OF DIFFERENTIAL GEOMETRY, 2008, 79 (01) : 111 - 139
[2] Construction of discrete constant mean curvature surfaces in Riemannian spaceforms and applications
Ogata, Yuta
Yasumoto, Masashi
[J]. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2017, 54 : 264 - 281
[3] Sub-Riemannian constant mean curvature surfaces in the Heisenberg group as limits
Ni Y.
[J]. Annali di Matematica Pura ed Applicata, 2004, 183 (4) : 555 - 570
[4] Constant Mean Curvature Spacelike Surfaces in Lorentzian Warped Products
Aledo, Juan A.
Rubio, Rafael M.
[J]. ADVANCES IN MATHEMATICAL PHYSICS, 2015, 2015
[5] SURFACES WITH CONSTANT MEAN CURVATURE
HILDERBR.S
[J]. MATHEMATISCHE ZEITSCHRIFT, 1969, 112 (02) : 107 - &
[6] SURFACES OF CONSTANT MEAN CURVATURE
WOLF, JA
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1966, 17 (05) : 1103 - &
[7] Surfaces with constant mean curvature
Perdomol, Oscar M.
[J]. BOLETIN DE MATEMATICAS, 2011, 18 (02): : 157 - 182
[8] Constant mean curvature surfaces
Meeks, William H., III
Perez, Joaquin
Tinaglia, Giuseppe
[J]. ADVANCES IN GEOMETRY AND MATHEMATICAL PHYSICS, 2016, 21 : 179 - +
[9] Constant mean curvature hypersurfaces in Riemannian manifolds
Pacard, Frank
[J]. RIVISTA DI MATEMATICA DELLA UNIVERSITA DI PARMA, 2005, 4 : 141 - 162
[10] Constant mean curvature spheres in Riemannian manifolds
F. Pacard
X. Xu
[J]. manuscripta mathematica, 2009, 128 : 275 - 295

← 1 2 3 4 5 →