New characteristics of infinitesimal isometry and Ricci solitons

Autor: I. G. Shandra, Sergey Stepanov
Rok vydání: 2012
Předmět:
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
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