Real hypersurfaces in the complex quadric with Reeb invariant Ricci tensor

被引：3

作者：

Suh, Young Jin ^{[1
,2
]}

Hwang, Doo Hyun ^{[1
,2
]}

Woo, Changhwa ^{[3
]}

机构：

[1] Kyungpook Natl Univ, Coll Nat Sci, Dept Math, Daegu 41566, South Korea

[2] Res Inst Real & Complex Manifolds, Daegu 41566, South Korea

[3] Woosuk Univ, Coll Nat Sci, Dept Math Educ, Wonju 55338, Jeonbuk, South Korea

来源：

JOURNAL OF GEOMETRY AND PHYSICS | 2017年 / 120卷

基金：

新加坡国家研究基金会;

关键词：

Reeb invariant Ricci tensor; (sic)-isotropic; (sic)-principal; Kahler structure; Complex conjugation; Complex quadric; HYPERBOLIC 2-PLANE GRASSMANNIANS; PROJECTIVE-SPACE; SUBMANIFOLDS;

D O I：

10.1016/j.geomphys.2017.05.012

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce the notion of Reeb invariant Ricci tensor for real hypersurfaces in the complex quadric Q(m) = SOm+2/SOmSO2. The Reeb invariant Ricci tensor implies that the unit normal vector field N becomes (sic)-principal or (sic)-isotropic. Then according to each case, we give a complete classification of real hypersurfaces in Q(m) = SOm+2/SOmSO2 with Reeb invariant Ricci tensor. (C) 2017 Elsevier B.V. All rights reserved.

引用

页码：96 / 105

页数：10

共 20 条

[1]

[Anonymous], 1987, Saitama Math. J.

[2] Commutativity of Cho and structure Jacobi operators of a real hypersurface in a complex projective space [J].

de Dios Perez, Juan .

ANNALI DI MATEMATICA PURA ED APPLICATA, 2015, 194 (06) :1781-1794

[3] Semi-parallel symmetric operators for Hopf hypersurfaces in complex two-plane Grassmannians [J].

Hwang, Doo Hyun ;

Lee, Hyunjin ;

Woo, Changhwa .

MONATSHEFTE FUR MATHEMATIK, 2015, 177 (04) :539-550

[4] REAL HYPERSURFACES AND COMPLEX SUBMANIFOLDS IN COMPLEX PROJECTIVE-SPACE [J].

KIMURA, M .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1986, 296 (01) :137-149

[5] Totally geodesic submanifolds of the complex quadric [J].

Klein, Sebastian .

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2008, 26 (01) :79-96

[6]

Kobayashi S, 1996, Foundations of differential geometry, V2

[7]

Pérez JD, 2001, ACTA MATH HUNG, V91, P343

[8]

Perez JDD, 1997, DIFFER GEOM APPL, V7, P211

[9]

Reckziegel H., 1996, Geometry and Topology of Submanifolds, VIII (Brussels 1995/Nordfjordeid, 1995), P302

[10] DIFFERENTIAL GEOMETRY OF COMPLEX HYPERSURFACES [J].

SMYTH, B .

ANNALS OF MATHEMATICS, 1967, 85 (02) :246-&

← 1 2 →