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We show that every five-dimensional Sasakian Lie algebra with trivial center is φ-symmetric. Moreover starting from a particular Sasakian structure on the Lie group S L(2, ℝ) × Aff(ℝ) we obtain a family of contact metric (k, μ) structures whose Boeckx invariants assume all values less than −1.
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Loiudice et al. (2018) studied this question.
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