New characteristics of infinitesimal isometry and Ricci solitons
Autor: | I. G. Shandra, Sergey Stepanov |
---|---|
Rok vydání: | 2012 |
Předmět: |
Pure mathematics
Curvature of Riemannian manifolds General Mathematics Mathematical analysis Ricci flow Riemannian manifold Isometry (Riemannian geometry) Levi-Civita connection symbols.namesake symbols Ricci decomposition Lie derivative Mathematics::Differential Geometry Ricci curvature Mathematics |
Zdroj: | Mathematical Notes. 92:422-425 |
ISSN: | 1573-8876 0001-4346 |
DOI: | 10.1134/s0001434612090155 |
Popis: | We prove that a vector field X on a compact Riemannian manifold (M, g) with Levi-Civita connection ∇ is an infinitesimal isometry if and only if it satisfies the system of differential equations: traceg(LX∇) = 0, traceg(LX Ric) = 0, where LX is the Lie derivative in the direction of X and Ric is the Ricci tensor. It follows from the second assertion that the Ricci soliton on a compact manifold M is trivial if its vector field X satisfies one of the following two conditions: traceg(LX Ric) ≤ 0 or traceg(LX Ric) ≥ 0. |
Databáze: | OpenAIRE |
Externí odkaz: |
načítá se...