Curvature tensors and Singer invariants of four-dimensional homogeneous spaces

Yuki Kiyota; Kazumi Tsukada

Commentationes Mathematicae Universitatis Carolinae (1999)

  • Volume: 40, Issue: 4, page 723-733
  • ISSN: 0010-2628

Abstract

top
We show that the Singer invariant of a four-dimensional homogeneous space is at most 1 .

How to cite

top

Kiyota, Yuki, and Tsukada, Kazumi. "Curvature tensors and Singer invariants of four-dimensional homogeneous spaces." Commentationes Mathematicae Universitatis Carolinae 40.4 (1999): 723-733. <http://eudml.org/doc/248407>.

@article{Kiyota1999,
abstract = {We show that the Singer invariant of a four-dimensional homogeneous space is at most $1$.},
author = {Kiyota, Yuki, Tsukada, Kazumi},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {homogeneous spaces; Singer invariant; locally homogeneous Riemannian space; Singer invariant; subspace of curvature tensors},
language = {eng},
number = {4},
pages = {723-733},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Curvature tensors and Singer invariants of four-dimensional homogeneous spaces},
url = {http://eudml.org/doc/248407},
volume = {40},
year = {1999},
}

TY - JOUR
AU - Kiyota, Yuki
AU - Tsukada, Kazumi
TI - Curvature tensors and Singer invariants of four-dimensional homogeneous spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1999
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 40
IS - 4
SP - 723
EP - 733
AB - We show that the Singer invariant of a four-dimensional homogeneous space is at most $1$.
LA - eng
KW - homogeneous spaces; Singer invariant; locally homogeneous Riemannian space; Singer invariant; subspace of curvature tensors
UR - http://eudml.org/doc/248407
ER -

References

top
  1. Bérard Bergery L., Les espaces homogènes riemanniens de dimension 4 , in Géométrie riemannienne en dimension (Séminaire A.Besse) Cedic, Paris (1981), pp.40-60. (1981) MR0769130
  2. Calvaruso G., Vanhecke L., Special ball-homogeneous spaces, Z. Anal. Anwendungen 16 (1997), 789-800. (1997) Zbl0892.53023MR1615680
  3. Calvaruso G., Vanhecke L., Ball-homogeneous spaces, Proc. Workshop on Recent Topics in Differential Geometry, Santiago de Compostela (1997). (1997) Zbl0892.53023
  4. Ishihara S., Homogeneous Riemannian spaces of four dimensions, J. Math. Soc. Japan 7 (1955), 345-370. (1955) Zbl0067.39602MR0082717
  5. Jensen G.R., Homogeneous Einstein spaces of dimension four, J. Differential Geom. 3 (1969), 309-349. (1969) Zbl0194.53203MR0261487
  6. Kiyota Y., Singer invariants of Riemannian homogeneous spaces, Master Thesis, Ochanomizu University (in Japanese) (1998). (1998) 
  7. Kowalski O., A note to a theorem by K. Sekigawa, Comment. Math. Univ. Carolinae 30 (1989), 85-88. (1989) Zbl0679.53043MR0995705
  8. Kowalski O., Prüfer F., Curvature tensors in dimension four which do not belong to any curvature homogeneous space, Arch. Math. 30 (1994), 45-57. (1994) MR1282112
  9. Kowalski O., Tricerri F., Vanhecke L., Curvature homogeneous Riemannian manifolds, J. Math. Pures Appl. 71 (1992), 471-501. (1992) Zbl0836.53029MR1193605
  10. Lastaria F.G., Metriche omogenee con la stessa curvatura, Tesi di dottorato di ricerca, University of Milano (1989). (1989) 
  11. Lastaria F.G., Homogeneous metrics with the same curvature, Simon Stevin 65 (1991), 267-281. (1991) Zbl0762.53034MR1162498
  12. Nicolodi L., Tricerri F., On two theorems of I.M. Singer about homogeneous spaces, Ann. Global Anal. Geom. 8 (1990), 193-209. (1990) Zbl0676.53058MR1088511
  13. Sekigawa K., Suga H., Vanhecke L., Curvature homogeneity for four-dimensional manifolds, J. Korean Math. Soc. 32 (1995), 93-101. (1995) Zbl0832.53031MR1321091
  14. Singer I.M., Infinitesimally homogeneous spaces, Comm. Pure Appl. Math. 13 (1960), 685-697. (1960) Zbl0171.42503MR0131248
  15. Takagi H., Conformally flat Riemannian manifolds admitting a transitive group of isometries, Tôhoku Math. J. 27 (1975), 103-110. (1975) Zbl0323.53037MR0442852

NotesEmbed ?

top

You must be logged in to post comments.