Geodesic
Left-invariant para-K\"ahler structures on six-dimensional nilpotent Lie groups
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 78 (2022), pp. 38-48

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Left-invariant para-complex structures on six-dimensional nilpotent Lie groups are considered. A complete list of six-dimensional nilpotent Lie groups that admit para-Kähler structures is obtained, explicit expressions for para-complex structures are found, and curvature properties of associated para-Kähler metrics are investigated. It is shown that paracomplex structures are nilpotent and the corresponding para-Kähler metrics are Ricci-flat.
Keywords: six-dimensional nilpotent Lie groups, symplectic Lie groups, left-invariant para-Kahler structures.
Mots-clés : para-complex structures 
@article{VTGU_2022_78_a2,
     author = {N. K. Smolentsev},
     title = {Left-invariant {para-K\"ahler} structures on six-dimensional nilpotent {Lie} groups},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {38--48},
     publisher = {mathdoc},
     number = {78},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2022_78_a2/}
}
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N. K. Smolentsev. Left-invariant para-K\"ahler structures on six-dimensional nilpotent Lie groups. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 78 (2022), pp. 38-48. http://geodesic.mathdoc.fr/item/VTGU_2022_78_a2/