Algebraic Properties of Curvature Operators in Lorentzian Manifolds with Large Isometry Groups

Symmetry Integrability and Geometry-Methods and Applications

article

Giovanni Calvaruso¹  Eduardo García-Río² 

[1] Dipartimento di Matematica E. De Giorgi, Università del Salento;Faculty of Mathematics, University of Santiago de Compostela

关键词: Lorentzian manifolds;    skew-symmetric curvature operator;    Jacobi;    Szab´o and skew-symmetric curvature operators;    commuting curvature operators;    IP manifolds;    Cspaces and P-spaces;   

DOI  :  10.3842/SIGMA.2010.005

来源: National Academy of Science of Ukraine

【 摘 要 】

Together with spaces of constant sectional curvature and products of a real line with a manifold of constant curvature, the socalled Egorov spaces and ε- spaces exhaust the class of n -dimensional Lorentzian manifolds admitting a group of isometries of dimension at least ½ n ( n −1)+1, for almost all values of n [Patrangenaru V., Geom. Dedicata 102 (2003), 25-33]. We shall prove that the curvature tensor of these spaces satisfy several interesting algebraic properties. In particular, we will show that Egorov spaces are Ivanov-Petrova manifolds, curvature-Ricci commuting (indeed, semi-symmetric) and P -spaces, and that ε-spaces are Ivanov-Petrova and curvature-curvature commuting manifolds.

【 授权许可】

Unknown