Conformally Osserman four-dimensional manifolds whose conformal Jacobi operators have complex eigenvalues

被引：14

作者：

Brozos-Vázquez, M ^{[1
]}

García-Rjo, E ^{[1
]}

Vázquez-Lorenzo, R ^{[1
]}

机构：

[1] Univ Santiago de Compostela, Fac Math, Dept Geometrie & Topol, Santiago De Compostela 15782, Spain

来源：

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2006年 / 462卷 / 2069期

关键词：

Jacobi operator; Weyl conformal tensor; conformally Osserman metric; Walker metric; self-duality; anti-self-duality;

D O I：

10.1098/rspa.2005.1621

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

Conformal Osserman four-dimensional manifolds are studied with special attention to the construction of new examples showing that the algebraic structure of any such curvature tenser can be realized at the differentiable level. As a consequence one gets examples of anti-self-dual manifolds whose anti-self-dual curvature operator has complex eigenvalues.

引用

页码：1425 / 1441

页数：17

共 27 条

[1]

ALEKSEEVSKI DM, 1999, ARCH MATH BRNO, V35, P193

[2] Osserman pseudo-Riemannian manifolds of signature (2,2) [J].

Blazic, N ;

Bokan, N ;

Rakic, Z .

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS, 2001, 71 :367-395

[3] A note on Osserman Lorentzian manifolds [J].

Blazic, N ;

Bokan, N ;

Gilkey, P .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 1997, 29 :227-230

[4] Conformally Osserman manifolds and conformally complex space forms [J].

Blazic, N ;

Gilkey, P .

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, 2004, 1 (1-2) :97-106

[5]

BLAZIC N, 2003, IN PRESS SPECTRAL GE

[6]

BLAZIE N, 2005, P DGA C CZECH REP 20

[7] Pseudo-Riemannian manifolds with simple Jacobi operators [J].

Bonome, A ;

Castro, R ;

García-Río, E ;

Hervella, L ;

Vázquez-Lorenzo, R .

JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 2002, 54 (04) :847-875

[8]

CHI QS, 1988, J DIFFER GEOM, V28, P187

[9] A note on the structure of algebraic curvature tensors [J].

Díaz-Ramos, JC ;

García-Río, E .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2004, 382 :271-277

[10] Anti-self-dual four-manifolds with a parallel real spinor [J].

Dunajski, M .

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2002, 458 (2021) :1205-1222

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