Geodesic
Lie triple systems and affinely connected spaces
Matematičeskie zametki, Tome 14 (1973) no. 1, pp. 107-112

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In this paper the author examines certain properties of affinely connected spaces whose curvature tensor satisfies precise conditions of an algebraic character. From the basic results obtained follow sufficiency conditions under which a compact Riemannian space is symmetric. 
@article{MZM_1973_14_1_a13,
     author = {P. I. Kovalev},
     title = {Lie triple systems and affinely connected spaces},
     journal = {Matemati\v{c}eskie zametki},
     pages = {107--112},
     publisher = {mathdoc},
     volume = {14},
     number = {1},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1973_14_1_a13/}
}
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P. I. Kovalev. Lie triple systems and affinely connected spaces. Matematičeskie zametki, Tome 14 (1973) no. 1, pp. 107-112. http://geodesic.mathdoc.fr/item/MZM_1973_14_1_a13/