Geodesic
Geodesic vectors and flat totally geodesic subalgebras in nilpotent metric Lie algebras
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, Tome 177 (2020), pp. 10-23

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We determine geodesics and flat totally geodesic subalgebras in higher-step nilpotent metric Lie algebras of dimension $5$. It is surprising that in nonfiliform metric Lie algebras with one-dimensional center, the geodesic vectors and flat totally geodesic subalgebras are independent of the choice of the inner product.
Keywords: nilpotent metric Lie algebra, geodesic vector, nonfiliform metric Lie algebras, flat totally geodesic subalgebras, inner product. 
@article{INTO_2020_177_a1,
     author = {A. Al-Abayechi and \'A. Figula},
     title = {Geodesic vectors and flat totally geodesic subalgebras in nilpotent metric {Lie} algebras},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {10--23},
     publisher = {mathdoc},
     volume = {177},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2020_177_a1/}
}
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A. Al-Abayechi; Á. Figula. Geodesic vectors and flat totally geodesic subalgebras in nilpotent metric Lie algebras. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, Tome 177 (2020), pp. 10-23. http://geodesic.mathdoc.fr/item/INTO_2020_177_a1/