Naturally reductive homogeneous spaces and generalized Heisenberg groups

F. Tricerri; L. Vanhecke

Compositio Mathematica (1984)

  • Volume: 52, Issue: 3, page 389-408
  • ISSN: 0010-437X

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Tricerri, F., and Vanhecke, L.. "Naturally reductive homogeneous spaces and generalized Heisenberg groups." Compositio Mathematica 52.3 (1984): 389-408. <http://eudml.org/doc/89672>.

@article{Tricerri1984,
author = {Tricerri, F., Vanhecke, L.},
journal = {Compositio Mathematica},
keywords = {naturally reductive spaces; generalized Heisenberg groups},
language = {eng},
number = {3},
pages = {389-408},
publisher = {Martinus Nijhoff Publishers},
title = {Naturally reductive homogeneous spaces and generalized Heisenberg groups},
url = {http://eudml.org/doc/89672},
volume = {52},
year = {1984},
}

TY - JOUR
AU - Tricerri, F.
AU - Vanhecke, L.
TI - Naturally reductive homogeneous spaces and generalized Heisenberg groups
JO - Compositio Mathematica
PY - 1984
PB - Martinus Nijhoff Publishers
VL - 52
IS - 3
SP - 389
EP - 408
LA - eng
KW - naturally reductive spaces; generalized Heisenberg groups
UR - http://eudml.org/doc/89672
ER -

References

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  2. [2] R. Brown and A. Gray: Vector cross products. Comment. Math. Helv.42 (1967) 222-236. Zbl0155.35702MR222105
  3. [3] J.E. D'Atri and H.K. Nickerson: Divergence-preserving geodesic symmetries. J. Differential Geometry3 (1969) 467-476. Zbl0195.23604MR262969
  4. [4] J.E. D'Atri and H.K. Nickerson: Geodesic symmetries in spaces with special curvature tensor. J. Differential Geometry9 (1974) 251-262. Zbl0285.53019MR394520
  5. [5] J.E. D'Atri: Geodesic spheres and symmetries in naturally reductive homogeneous spaces. Michigan Math. J.22 (1975) 71-76. Zbl0317.53045MR372786
  6. [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. Zbl0404.53044MR519928
  7. [7] A. Gray: Riemannian manifolds with geodesic symmetries of order 3. J. Differential Geometry7 (1972) 343-369. Zbl0275.53026MR331281
  8. [8] A. Kaplan: Riemannian nilmanifolds attached to Clifford modules. Geometriae Dedicata1 (1981) 127-136. Zbl0495.53046MR621376
  9. [9] A. Kaplan: On the geometry of groups of Heisenberg type, to appear in Bull. London Math. Soc. Zbl0521.53048MR686346
  10. [10] S. Kobayashi and K. Nomizu: Foundations of differential geometry, I, II. Interscience Publishers, New York (1963 and 1969). Zbl0119.37502MR152974
  11. [11] O. Kowalski: Generalized symmetric spaces, Lecture Notes in Mathematics, 805. Springer-Verlag, Berlin/Heidelberg/ New York (1980). Zbl0431.53042MR579184
  12. [12] E. Kurcius: 6-dimensional generalized symmetric Riemannian spaces. Ph.D. Thesis, University of Katowice (1978). 
  13. [13] J. Szenthe: Sur la connection naturelle à torsion nulle. Acta Sci. Math. (Szeged) 38 (1976) 383-398. Zbl0321.53029MR431042
  14. [14] F. Tricerri and L. Vanhecke: Homogeneous structures on Riemannian manifolds, Lecture Note Series of the London Math. Soc., 83. Cambridge Univ. Press (1983). Zbl0509.53043MR712664
  15. [15] L. Vanhecke: Some solved and unsolved problems about harmonic and commutative spaces, to appear in Bull. Soc. Math. Belg. Zbl0518.53042MR683378
  16. [16] L. Vanhecke and T.J. Willmore: Interaction of tubes and spheres, to appear. Zbl0491.53034MR697328
  17. [17] J. Wolf: The geometry and structure of isotropy irreducible homogeneous spaces, Acta Math.120 (1968) 59-148. Zbl0157.52102MR223501

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