On the Riemannian geometry of the nilpotent groups $H(p,r)$
HTML articles powered by AMS MathViewer
- by Paola Piu and Michel Goze PDF
- Proc. Amer. Math. Soc. 119 (1993), 611-619 Request permission
Abstract:
We study some aspect of the left-invariant Riemannian geometry on a class of nilpotent Lie groups $H(p,r)$ that generalize the Heisenberg group ${H_{2p + 1}}$. Let us prove that the groups of type $H$ (or Kaplan’s spaces) and the $H(p,r)$ groups have same common Riemannian properties but they are not the same spaces.References
- J. E. D’Atri and H. K. Nickerson, Geodesic symmetries in spaces with special curvature tensors, J. Differential Geometry 9 (1974), 251–262. MR 394520 M. Goze, Étude locale des systèmes de Pfaff, Publ. IRMA, Strasbourg, 1989.
- Michel Goze, Systèmes de Pfaff associés aux algèbres de Lie de type $H$, Rend. Sem. Mat. Univ. Politec. Torino 46 (1988), no. 1, 91–110 (1990) (French). MR 1084140
- Michel Goze and Yuri Haraguchi, Sur les $r$-systèmes de contact, C. R. Acad. Sci. Paris Sér. I Math. 294 (1982), no. 2, 95–97 (French, with English summary). MR 651795
- Michel Goze and Paola Piu, Classification des métriques invariantes à gauche sur le groupe de Heisenberg, Rend. Circ. Mat. Palermo (2) 39 (1990), no. 2, 299–306 (French, with English summary). MR 1106594, DOI 10.1007/BF02844764 Y. Haraguchi, Sur une généralisation des structures de contact, Thèse, Mulhouse, 1981.
- Gary R. Jensen, Homogeneous Einstein spaces of dimension four, J. Differential Geometry 3 (1969), 309–349. MR 261487
- Aroldo Kaplan, On the geometry of groups of Heisenberg type, Bull. London Math. Soc. 15 (1983), no. 1, 35–42. MR 686346, DOI 10.1112/blms/15.1.35
- Wilfred Reyes, A note about Killing vector fields on $H(p,r)$, Rend. Sem. Fac. Sci. Univ. Cagliari 55 (1985), no. 1, 25–29 (English, with Italian summary). MR 849723
- F. Tricerri and L. Vanhecke, Homogeneous structures on Riemannian manifolds, London Mathematical Society Lecture Note Series, vol. 83, Cambridge University Press, Cambridge, 1983. MR 712664, DOI 10.1017/CBO9781107325531
Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 119 (1993), 611-619
- MSC: Primary 53C30; Secondary 22E25
- DOI: https://doi.org/10.1090/S0002-9939-1993-1189548-9
- MathSciNet review: 1189548