Nonhomogeneous Riemannian 3-manifolds with distinct constant Ricci eigenvalues

Oldřich Kowalski

Commentationes Mathematicae Universitatis Carolinae (1993)

  • Volume: 34, Issue: 3, page 451-457
  • ISSN: 0010-2628

Abstract

top
We extend a construction by K. Yamato [Ya] to obtain new explicit examples of Riemannian 3-manifolds as in the title. Some of these examples have an interesting geometrical interpretation.

How to cite

top

Kowalski, Oldřich. "Nonhomogeneous Riemannian 3-manifolds with distinct constant Ricci eigenvalues." Commentationes Mathematicae Universitatis Carolinae 34.3 (1993): 451-457. <http://eudml.org/doc/247456>.

@article{Kowalski1993,
abstract = {We extend a construction by K. Yamato [Ya] to obtain new explicit examples of Riemannian 3-manifolds as in the title. Some of these examples have an interesting geometrical interpretation.},
author = {Kowalski, Oldřich},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Riemannian manifold; curvature homogeneous space; curvature homogeneous; homogeneous model space; Ricci eigenvalues},
language = {eng},
number = {3},
pages = {451-457},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Nonhomogeneous Riemannian 3-manifolds with distinct constant Ricci eigenvalues},
url = {http://eudml.org/doc/247456},
volume = {34},
year = {1993},
}

TY - JOUR
AU - Kowalski, Oldřich
TI - Nonhomogeneous Riemannian 3-manifolds with distinct constant Ricci eigenvalues
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1993
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 34
IS - 3
SP - 451
EP - 457
AB - We extend a construction by K. Yamato [Ya] to obtain new explicit examples of Riemannian 3-manifolds as in the title. Some of these examples have an interesting geometrical interpretation.
LA - eng
KW - Riemannian manifold; curvature homogeneous space; curvature homogeneous; homogeneous model space; Ricci eigenvalues
UR - http://eudml.org/doc/247456
ER -

References

top
  1. Boeckx E., Kowalski O., Vanhecke L., Nonhomogeneous relatives of symmetric spaces, to appear in Differential Geometry and its Applications. MR1264908
  2. Kowalski O., A classification of Riemannian 3-manifolds with constant principal Ricci curvatures ϱ 1 = ϱ 2 ≠ ϱ 3 , to appear in Nagoya Math. J. MR1253692
  3. Kobayashi S., Nomizu K., Foundations of Differential Geometry I, Interscience Publishers, New York, 1983. Zbl0119.37502
  4. Kowalski O., Tricerri F., Vanhecke L., New examples of non-homogeneous Riemannian manifolds whose curvature tensor is that of a Riemannian symmetric space, C.R. Acad. Sci. Paris, Sér. I, 311 (1990), 355-360. (1990) Zbl0713.53028MR1071643
  5. Kowalski O., Tricerri F., Vanhecke L., Curvature homogeneous Riemannian manifolds, J. Math. Pures Appl. 71 (1992), 471-501. (1992) Zbl0836.53029MR1193605
  6. Kowalski O., Tricerri F., Vanhecke L., Curvature homogeneous spaces with a solvable Lie group as homogeneous model, J. Math. Soc. Japan 44 (1992), 461-484. (1992) Zbl0762.53031MR1167378
  7. Milnor J., Curvatures of left invariant Lie groups, Adv. in Math. 21 (1976), 293-329. (1976) MR0425012
  8. Sekigawa K., On some 3-dimensional Riemannian manifolds, Hokkaido Math. J. 2 (1973), 259-270. (1973) Zbl0266.53034MR0353204
  9. Sekigawa K., On some 3-dimensional curvature homogeneous spaces, Tensor, N.S. 31 (1977), 87-97. (1977) Zbl0356.53016MR0464115
  10. Singer I.M., Infinitesimally homogeneous spaces, Comm. Pure Appl. Math. 13 (1960), 685-697. (1960) Zbl0171.42503MR0131248
  11. Tsukada T., Curvature homogeneous hypersurfaces immersed in a real space form, Tôhoku Math. J. 40 (1988), 221-244. (1988) Zbl0651.53037MR0943821
  12. Yamato K., A characterization of locally homogeneous Riemannian manifolds of dimension 3, Nagoya Math. J. 123 (1991), 77-90. (1991) MR1126183

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.