The curvature tensor of (\ka,μ,ν)-contact metric manifolds

Kadri Arslan; Alfonso Carriazo; Verónica Martín-Molina; Cengizhan Murathan

doi:10.1007/s00605-015-0762-3

paper

The curvature tensor of (\ka,μ,ν)-contact metric manifolds

arXiv:1109.6258 · doi:10.1007/s00605-015-0762-3

Abstract

We study the Riemann curvature tensor of (κ,μ,ν)-contact metric manifolds, which we prove to be completely determined in dimension 3, and we observe how it is affected by D_a-homothetic deformations. This prompts the definition and study of generalized (κ,μ,ν)-space forms and of the necessary and sufficient conditions for them to be conformally flat.