Osaka Journal of Mathematics

On five dimensional Sasakian Lie algebras with trivial center

E. Loiudice and A. Lotta

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Abstract

We show that every five-dimensional Sasakian Lie algebra with trivial center is $\varphi$-symmetric. Moreover starting from a particular Sasakian structure on the Lie group $SL(2,\mathbb{R})\times\text{Aff}(\mathbb{R})$ we obtain a family of contact metric $(k,\mu)$ structures whose Boeckx invariants assume all values less than $-1$.

Article information

Source
Osaka J. Math., Volume 55, Number 1 (2018), 39-49.

Dates
First available in Project Euclid: 11 January 2018

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1515661215

Mathematical Reviews number (MathSciNet)
MR3744974

Zentralblatt MATH identifier
06848742

Subjects
Primary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.) 22E60: Lie algebras of Lie groups {For the algebraic theory of Lie algebras, see 17Bxx}
Secondary: 53C30: Homogeneous manifolds [See also 14M15, 14M17, 32M10, 57T15] 53C35: Symmetric spaces [See also 32M15, 57T15]

Citation

Loiudice, E.; Lotta, A. On five dimensional Sasakian Lie algebras with trivial center. Osaka J. Math. 55 (2018), no. 1, 39--49. https://projecteuclid.org/euclid.ojm/1515661215


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