# Three-dimensional conformally flat pseudo-symmetric spaces of constant type

Norio Hashimoto; Masami Sekizawa

Archivum Mathematicum (2000)

- Volume: 036, Issue: 4, page 279-286
- ISSN: 0044-8753

## Access Full Article

top## Abstract

top## How to cite

topHashimoto, Norio, and Sekizawa, Masami. "Three-dimensional conformally flat pseudo-symmetric spaces of constant type." Archivum Mathematicum 036.4 (2000): 279-286. <http://eudml.org/doc/248525>.

@article{Hashimoto2000,

abstract = {An explicit classification of the spaces in the title is given. The resulting spaces are locally products or locally warped products of the real line and two-dimensional spaces of constant curvature.},

author = {Hashimoto, Norio, Sekizawa, Masami},

journal = {Archivum Mathematicum},

keywords = {Riemannian manifold; conformally flat space; pseudo-symmetric space; warped product; Riemannian manifold; pseudo-Riemannian space; conformally flat},

language = {eng},

number = {4},

pages = {279-286},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {Three-dimensional conformally flat pseudo-symmetric spaces of constant type},

url = {http://eudml.org/doc/248525},

volume = {036},

year = {2000},

}

TY - JOUR

AU - Hashimoto, Norio

AU - Sekizawa, Masami

TI - Three-dimensional conformally flat pseudo-symmetric spaces of constant type

JO - Archivum Mathematicum

PY - 2000

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 036

IS - 4

SP - 279

EP - 286

AB - An explicit classification of the spaces in the title is given. The resulting spaces are locally products or locally warped products of the real line and two-dimensional spaces of constant curvature.

LA - eng

KW - Riemannian manifold; conformally flat space; pseudo-symmetric space; warped product; Riemannian manifold; pseudo-Riemannian space; conformally flat

UR - http://eudml.org/doc/248525

ER -

## References

top- Boeckx E., Kowalski O., Vanhecke L., Riemannian Manifold of Conullity Two, World Scientific, Singapore, 1996. (1996) MR1462887
- Deprez J., Deszcz R., Verstraelen L., Examples of pseudo-symmetric conformally flat warped products, Chinese J. Math 17(1989), 51–65. (1989) Zbl0678.53022MR1007875
- Deszcz R., On pseudo-symmetric spaces, Bull. Soc. Math. Belgium, Série A. 44(1992), 1–34. (1992)
- Eisenhart L. P., Riemannian Geometry, Princeton University, Sixth Printing 1966. (First Printing 1925.) (1966) MR1487892
- Hájková V., Foliated semi-symmetric spaces in dimension 3, (in Czech), Doctoral Thesis, Prague, 1995. (1995)
- Kowalski O., A classification of Riemannian 3-manifolds with constant principal Ricci curvatures ${\rho}_{1}={\rho}_{2}\ne {\rho}_{3}$, Nagoya Math. J. 132(1993), 1–36. (1993) MR1253692
- Kowalski O., An explicit classification of 3-dimensional Riemannian spaces satisfying $R(X,Y)\xb7R=0$, Czechoslovak Math. J. 46(121) (1996), 427–474. (Preprint 1991). (1996) Zbl0879.53014MR1408298
- Kowalski O., Sekizawa M., Locally isometry classes of Riemannian 3-manifolds with constant Ricci eigenvalues ${\rho}_{1}={\rho}_{2}\ne {\rho}_{3}>0$, Arch. Math. 32(1996), 137–145. (1996) MR1407345
- Kowalski O., Sekizawa M., Riemannian 3-manifolds with $c$-conullity two, Bollenttino, U.M.I., (7)11-B (1997), Suppl. face. 2, 161–184. (1997) Zbl0879.53034MR1456259
- Kowalski O., Sekizawa M., Pseudo-symmetric spaces of constant type in dimension three-elliptic spaces, Rendiconti di Matematica, Serie VII, Vol.17, Roma (1997), 477–512. (1997) Zbl0889.53026MR1608724
- Kowalski O., Sekizawa M., Pseudo-symmetric spaces of constant type in dimension three-non-elliptic spaces, Bull. Tokyo Gakugei University Sect.IV. 50(1998), 1–28. (1998) Zbl0945.53020MR1656076
- Kowalski O., Sekizawa M., Pseudo-symmetric Spaces of Constant Type in Dimension Three, Personal Note, Charles University-Tokyo Gakugei University, Prague-Tokyo, 1998. (1998) Zbl0945.53020
- Mikeš J., Geodesic mappings of affine-connected and Riemannian spaces, J. Math. Sci., New York 1996, 311–333. (1996) Zbl0866.53028MR1384327
- Milnor J., Curvatures of left invarinat metrics on Lie groups, Adv. Math. 21(1976), 293–329. (1976) MR0425012
- O’Neill B., Semi-Riemannian Geometry With Applications to Relativity, Academic Press, New York-London, 1983. (1983) Zbl0531.53051MR0719023
- Takagi H., Conformally flat Riemannian manifolds admitting a transitive group of isometries, Tôhoku Math. Journ. 27(1975), 103–110. (1975) Zbl0323.53037MR0442852

## Citations in EuDML Documents

top- Giovanni Calvaruso, Conformally flat pseudo-symmetric spaces of constant type
- Giovanni Calvaruso, Conformally flat semi-symmetric spaces
- Giovanni Calvaruso, Conformally flat Lorentzian three-spaces with various properties of symmetry and homogeneity
- N. Malekzadeh, E. Abedi, U.C. De, Pseudosymmetric and Weyl-pseudosymmetric $(\kappa ,\mu )$-contact metric manifolds

## NotesEmbed ?

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