The geometry of modified Riemannian extensions

被引：40

作者：

Calvino-Louzao, E. ^{[1
]}

Garcia-Rio, E. ^{[1
]}

Gilkey, P. ^{[2
]}

Vazquez-Lorenzo, R. ^{[1
]}

机构：

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

[2] Univ Oregon, Dept Math, Eugene, OR 97403 USA

来源：

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2009年 / 465卷 / 2107期

关键词：

affine connection; Einstein; Jacobi operator; para-Kaehler; Osserman manifold; modified Riemannian extension; OSSERMAN METRICS; JACOBI; NILPOTENT; MANIFOLDS; CONNECTIONS; OPERATORS;

D O I：

10.1098/rspa.2009.0046

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：

We show that every paracomplex space form is locally isometric to a modified Riemannian extension and gives necessary and sufficient conditions for a modified Riemannian extension to be Einstein. We exhibit Riemannian extension Osserman manifolds of signature (3, 3), whose Jacobi operators have non-trivial Jordan normal form and which are not nilpotent. We present new four-dimensional results in Osserman geometry.

引用

页码：2023 / 2040

页数：18

共 38 条

[1]

Afifi Z., 1954, Q. J. Math, V5, P312, DOI [10.1093/qmath/5.1.312, DOI 10.1093/QMATH/5.1.312]

[2]

ALEKSEEVSKY DV, J REINE ANG IN PRESS

[3]

[Anonymous], 1997, B SOC MATH FR

[4] 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

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

Blazic, N ;

Bokan, N ;

Gilkey, P .

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

[6]

BOKAN N, 1990, REND CIRC MAT PALERM, V39, P331, DOI DOI 10.1007/BF02844767

[7] Nonsymmetric Osserman indefinite Kahler manifolds [J].

Bonome, A ;

Castro, R ;

Garcia-Rio, E ;

Hervella, L ;

Vazquez-Lorenzo, R .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1998, 126 (09) :2763-2769

[8] Conformally Osserman four-dimensional manifolds whose conformal Jacobi operators have complex eigenvalues [J].

Brozos-Vázquez, M ;

García-Rjo, E ;

Vázquez-Lorenzo, R .

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2006, 462 (2069) :1425-1441

[9]

CALVINOLOUZAO E, CAN J MATH IN PRESS

[10]

Cortés V, 2004, J HIGH ENERGY PHYS

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