On the curvature of certain extensions of $H$-type groups
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- by Isabel Dotti
- Proc. Amer. Math. Soc. 125 (1997), 573-578
- DOI: https://doi.org/10.1090/S0002-9939-97-03576-4
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Abstract:
We show that a one-dimensional solvable extension of an H-type group is symmetric if and only if it has negative curvature.References
- Jorge Boggino, Generalized Heisenberg groups and solvmanifolds naturally associated, Rend. Sem. Mat. Univ. Politec. Torino 43 (1985), no. 3, 529–547 (1986). MR 884876
- Berndt J., Tricerri F., Vanhecke L., Generalized Heisenberg groups and Damek-Ricci harmonic spaces, Lecture Notes in Mathematics 1598, Springer Verlag, Berlin-Heidelberg 1995.
- Michael Cowling, Anthony H. Dooley, Adam Korányi, and Fulvio Ricci, $H$-type groups and Iwasawa decompositions, Adv. Math. 87 (1991), no. 1, 1–41. MR 1102963, DOI 10.1016/0001-8708(91)90060-K
- Ewa Damek, Curvature of a semidirect extension of a Heisenberg type nilpotent group, Colloq. Math. 53 (1987), no. 2, 249–253. MR 924069, DOI 10.4064/cm-53-2-249-253
- Ewa Damek and Fulvio Ricci, Harmonic analysis on solvable extensions of $H$-type groups, J. Geom. Anal. 2 (1992), no. 3, 213–248. MR 1164603, DOI 10.1007/BF02921294
- Carolyn Gordon, Isospectral closed Riemannian manifolds which are not locally isometric, J. Differential Geom. 37 (1993), no. 3, 639–649. MR 1217163
- Ernst Heintze, On homogeneous manifolds of negative curvature, Math. Ann. 211 (1974), 23–34. MR 353210, DOI 10.1007/BF01344139
- Aroldo Kaplan, Fundamental solutions for a class of hypoelliptic PDE generated by composition of quadratic forms, Trans. Amer. Math. Soc. 258 (1980), no. 1, 147–153. MR 554324, DOI 10.1090/S0002-9947-1980-0554324-X
- Lanzendorf M., Einstein metrics with nonpositive sectional curvature on extensions of Lie algebras of Heisenberg type, preprint, July 1995.
- Z. I. Szabo, Spectral theory for operator families on Riemannian manifolds, Differential geometry: Riemannian geometry (Los Angeles, CA, 1990) Proc. Sympos. Pure Math., vol. 54, Amer. Math. Soc., Providence, RI, 1993, pp. 615–665. MR 1216651, DOI 10.1090/pspum/054.3/1216651
Bibliographic Information
- Isabel Dotti
- Affiliation: FaMAF, Universidad Nacional de Córdoba, 5000 Córdoba, Argentina
- Email: idotti@mate.uncor.edu
- Received by editor(s): February 13, 1995
- Received by editor(s) in revised form: August 16, 1995
- Additional Notes: Partially supported by grants from Conicor, SECYTUNC (Argentina), and I.C.T.P. (Trieste)
- Communicated by: Roe Goodman
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 573-578
- MSC (1991): Primary 53C25
- DOI: https://doi.org/10.1090/S0002-9939-97-03576-4
- MathSciNet review: 1350939
Dedicated: Dedicated to the memory of Franco Tricerri