Naturality of homogeneous metrics on Stiefel manifolds SO(m+1)/SO(m-1)

被引：15

作者：

Abbassi, Mohamed Tahar Kadaoui ^{[2
]}

Kowalski, Oldrich ^{[1
]}

机构：

[1] Charles Univ Prague, Fac Math & Phys, Prague 18675 8, Czech Republic

[2] Univ Sidi Mohamed Ben Abdallah, Fac Sci Dhar El Mahraz, Dept Math, Fes, Fes, Morocco

来源：

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS | 2010年 / 28卷 / 02期

关键词：

Unit tangent (sphere) bundle; g-natural metric; TANGENT SPHERE BUNDLES; UNIT VECTOR-FIELDS; CURVATURE; VOLUME; ENERGY;

D O I：

10.1016/j.difgeo.2009.05.007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It is well known that the unit tangent sphere bundle T1Sm of the standard sphere S-m can be naturally identified with the Stiefel manifold V2Rm+1 = SO(m + 1)/SO(m - 1). In this paper, we construct the (1-1) correspondence between all SO(m + 1)-invariant homogeneous metrics oil V2Rm+1 and all so-called g-natural metrics oil T1Sm. (C) 2009 Elsevier B.V. All rights reserved.

引用

页码：131 / 139

页数：9

共 43 条

[1] g-natural contact metrics on unit tangent sphere bundles [J].

Abbassi, M. T. K. ;

Calvaruso, G. .

MONATSHEFTE FUR MATHEMATIK, 2007, 151 (02) :89-109

[2] Harmonicity of unit vector fields with respect to Riemannian g-natural metrics [J].

Abbassi, M. T. K. ;

Calvaruso, G. ;

Perrone, D. .

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2009, 27 (01) :157-169

[3] On Riemannian g-natural metrics of the form a.gs+b.gh+c.gv on the tangent bundle of a Riemannian manifold (M,g) [J].

Abbassi, Mohamed Tahar Kadaoui ;

Sarih, Maati .

MEDITERRANEAN JOURNAL OF MATHEMATICS, 2005, 2 (01) :19-43

[4] On some hereditary properties of Riemannian g-natural metrics on tangent bundles of Riemannian manifolds [J].

Abbassi, MTK ;

Sarih, M .

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2005, 22 (01) :19-47

[5]

[Anonymous], 1998, Period. Math. Hungar.

[6]

[Anonymous], 2001, INT J MATH MATH SCI, DOI DOI 10.1155/S0161171201002009

[7]

[Anonymous], 1962, J REINE ANGEW MATH

[8]

[Anonymous], 2002, RIEMANNIAN GEOMETRY

[9] CRITICAL ASSOCIATED METRICS ON CONTACT MANIFOLDS [J].

BLAIR, DE .

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS, 1984, 37 (AUG) :82-88

[10] CRITICAL ASSOCIATED METRICS ON CONTACT MANIFOLDS .3. [J].

BLAIR, DE .

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS, 1991, 50 :189-196

← 1 2 3 4 5 →