Available in electronic format
Available in print format
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
     

On the curvature of certain extensions of $H$-type groups

Author(s): Isabel Dotti
Journal: Proc. Amer. Math. Soc. 125 (1997), 573-578.
MSC (1991): Primary 53C25
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

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:

[B]
Boggino J., Generalized Heisenberg groups and solvmanifolds naturally associated, Rend. Sem. Mat. Univers. Politecn. Torino, 43 (1985), 529-547. MR 88f:53093

[BTV]
Berndt J., Tricerri F., Vanhecke L., Generalized Heisenberg groups and Damek-Ricci harmonic spaces, Lecture Notes in Mathematics 1598, Springer Verlag, Berlin-Heidelberg 1995.

[C]
Cowling M., Dooley A., Korányi A., Ricci F., H-type groups and Iwasawa decompositions, Advances in Math. 87 (1991) 1-41. MR 92e:22017

[D]
Damek E., Curvature of a semidirect extension of a Heisenberg type nilpotent group, Coll. Math. 53 (1987) 249-253. MR 89d:22007

[DR]
Damek E., Ricci F., Harmonic analysis on solvable extensions of H-type groups, Journal of Geometric Analysis, 2 (1992) 213-248. MR 93d:43006

[G]
Gordon C., Isospectral closed riemannian manifolds which are not locally isometric, Jour. Diff. Geom. 37 (1993), 639-649. MR 94b:58098

[H]
Heintze E., On homogeneous manifolds of negative curvature, Math. Ann. 211 (1974) 23-34. MR 50:5695

[K]
Kaplan A., Fundamental solutions for a class of hypoelliptic operators, Trans. Amer. Math. Society 258 (1980) 147-153. MR 81c:58059

[L]
Lanzendorf M., Einstein metrics with nonpositive sectional curvature on extensions of Lie algebras of Heisenberg type, preprint, July 1995.

[S]
Szabo Z., Spectral theory for operator families on riemannian manifolds, Proceedings of Symposia in Pure Mathematics, Volume 54, (1993) 615-665. MR 94k:58152


Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 53C25

Retrieve articles in all Journals with MSC (1991): 53C25


Additional Information:

Isabel Dotti
Affiliation: FaMAF, Universidad Nacional de Córdoba, 5000 Córdoba, Argentina
Email: idotti@mate.uncor.edu

DOI: 10.1090/S0002-9939-97-03576-4
PII: S 0002-9939(97)03576-4
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)
Dedicated: Dedicated to the memory of Franco Tricerri
Communicated by: Roe Goodman
Copyright of article: Copyright 1997, American Mathematical Society


  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement
Search the AMSPowered by Google