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

• Опубліковано в: : Symmetry, Integrability and Geometry: Methods and Applications
• Дата: 2010
• Автори: Calvaruso, G., García-Río, E.
• Формат: Стаття
• Мова: English
• Опубліковано: Інститут математики НАН України 2010
• Онлайн доступ: https://nasplib.isofts.kiev.ua/handle/123456789/146096
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Цитувати: Algebraic Properties of Curvature Operators in Lorentzian Manifolds with Large Isometry Groups / E. García-Río // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 22 назв. — англ.

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 0.5n(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 satisfi 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.