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

Abstract

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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.

How to cite

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Hashimoto, 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

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  8. Kowalski O., Sekizawa M., Locally isometry classes of Riemannian 3-manifolds with constant Ricci eigenvalues ρ 1 = ρ 2 ≠ ρ 3 > 0 , Arch. Math. 32(1996), 137–145. (1996) MR1407345
  9. 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
  10. 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
  11. 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
  12. 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
  13. Mikeš J., Geodesic mappings of affine-connected and Riemannian spaces, J. Math. Sci., New York 1996, 311–333. (1996) Zbl0866.53028MR1384327
  14. Milnor J., Curvatures of left invarinat metrics on Lie groups, Adv. Math. 21(1976), 293–329. (1976) MR0425012
  15. O’Neill B., Semi-Riemannian Geometry With Applications to Relativity, Academic Press, New York-London, 1983. (1983) Zbl0531.53051MR0719023
  16. Takagi H., Conformally flat Riemannian manifolds admitting a transitive group of isometries, Tôhoku Math. Journ. 27(1975), 103–110. (1975) Zbl0323.53037MR0442852

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