no. 3
Naturally reductive homogeneous spaces and generalized Heisenberg groups
Compositio Mathematica, Tome 52 (1984) no. 3, pp. 389-408. 
@article{CM_1984__52_3_389_0,
     author = {Tricerri, F. and Vanhecke, L.},
     title = {Naturally reductive homogeneous spaces and generalized {Heisenberg} groups},
     journal = {Compositio Mathematica},
     pages = {389--408},
     publisher = {Martinus Nijhoff Publishers},
     volume = {52},
     number = {3},
     year = {1984},
     mrnumber = {756730},
     zbl = {0551.53028},
     language = {en},
     url = {http://www.numdam.org/item/CM_1984__52_3_389_0/}
}
TY  - JOUR
AU  - Tricerri, F.
AU  - Vanhecke, L.
TI  - Naturally reductive homogeneous spaces and generalized Heisenberg groups
JO  - Compositio Mathematica
PY  - 1984
SP  - 389
EP  - 408
VL  - 52
IS  - 3
PB  - Martinus Nijhoff Publishers
UR  - http://www.numdam.org/item/CM_1984__52_3_389_0/
LA  - en
ID  - CM_1984__52_3_389_0
ER  - 
%0 Journal Article
%A Tricerri, F.
%A Vanhecke, L.
%T Naturally reductive homogeneous spaces and generalized Heisenberg groups
%J Compositio Mathematica
%D 1984
%P 389-408
%V 52
%N 3
%I Martinus Nijhoff Publishers
%U http://www.numdam.org/item/CM_1984__52_3_389_0/
%G en
%F CM_1984__52_3_389_0
Tricerri, F.; Vanhecke, L. Naturally reductive homogeneous spaces and generalized Heisenberg groups. Compositio Mathematica, Tome 52 (1984) no. 3, pp. 389-408. http://www.numdam.org/item/CM_1984__52_3_389_0/

[1] W. Ambrose and I.M. Singer: On homogeneous Riemannian manifolds. Duke Math. J. 25 (1958) 647-669. | MR | Zbl

[2] R. Brown and A. Gray: Vector cross products. Comment. Math. Helv. 42 (1967) 222-236. | MR | Zbl

[3] J.E. D'Atri and H.K. Nickerson: Divergence-preserving geodesic symmetries. J. Differential Geometry 3 (1969) 467-476. | MR | Zbl

[4] J.E. D'Atri and H.K. Nickerson: Geodesic symmetries in spaces with special curvature tensor. J. Differential Geometry 9 (1974) 251-262. | MR | Zbl

[5] J.E. D'Atri: Geodesic spheres and symmetries in naturally reductive homogeneous spaces. Michigan Math. J. 22 (1975) 71-76. | MR | Zbl

[6] J.E. D'Atri: and W. Ziller: Naturally reductive metrics and Einstein metrics on compact Lie Groups. Mem. Amer. Math. Soc. 18 (1979) 215. | MR | Zbl

[7] A. Gray: Riemannian manifolds with geodesic symmetries of order 3. J. Differential Geometry 7 (1972) 343-369. | MR | Zbl

[8] A. Kaplan: Riemannian nilmanifolds attached to Clifford modules. Geometriae Dedicata 1 (1981) 127-136. | MR | Zbl

[9] A. Kaplan: On the geometry of groups of Heisenberg type, to appear in Bull. London Math. Soc. | MR | Zbl

[10] S. Kobayashi and K. Nomizu: Foundations of differential geometry, I, II. Interscience Publishers, New York (1963 and 1969). | MR | Zbl

[11] O. Kowalski: Generalized symmetric spaces, Lecture Notes in Mathematics, 805. Springer-Verlag, Berlin/Heidelberg/ New York (1980). | MR | Zbl

[12] E. Kurcius: 6-dimensional generalized symmetric Riemannian spaces. Ph.D. Thesis, University of Katowice (1978).

[13] J. Szenthe: Sur la connection naturelle à torsion nulle. Acta Sci. Math. (Szeged) 38 (1976) 383-398. | MR | Zbl

[14] F. Tricerri and L. Vanhecke: Homogeneous structures on Riemannian manifolds, Lecture Note Series of the London Math. Soc., 83. Cambridge Univ. Press (1983). | MR | Zbl

[15] L. Vanhecke: Some solved and unsolved problems about harmonic and commutative spaces, to appear in Bull. Soc. Math. Belg. | MR | Zbl

[16] L. Vanhecke and T.J. Willmore: Interaction of tubes and spheres, to appear. | MR | Zbl

[17] J. Wolf: The geometry and structure of isotropy irreducible homogeneous spaces, Acta Math. 120 (1968) 59-148. | MR | Zbl