Curvature homogeneous spaces with a solvable Lie group as homogeneous model

Oldrich KOWALSKI; Franco TRICERRI; Lieven VANHECKE

doi:10.2969/jmsj/04430461

Oldrich KOWALSKI, Franco TRICERRI, Lieven VANHECKE

Author information

JOURNAL FREE ACCESS

1992 Volume 44 Issue 3 Pages 461-484

DOI https://doi.org/10.2969/jmsj/04430461

Details

Published: 1992 Received: July 31, 1991 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
Correction information
Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) L. Bérard-Bergery, Les espaces homogènes riemanniens de dimension 4, Géométrie riemannienne en dimension 4, Séminaire A. Besse, Cedic, Paris, 1981, pp. 40-60.
2) M. Berger, L'oeuvre d'André Lichnerowicz en géométrie riemannienne, Physique quantique et géométrie (eds. D. Bernard and Y. Choquet-Bruhat), Colloque Géométrie et Physique 1986 en l'honneur d'André Lichnerowicz, Travaux en Cours, Hermann, Paris, 1988, pp. 11-24.
3) R. L. Bishop and B. O' Neill, Manifolds of negative curvature, Trans. Amer. Math. Soc., 145 (1969), 1-49.
4) D. Ferus, H. Karcher and H. F. Münzner, Cliffordalgebren und neue isoparametrische Hyperflächen, Math. Z., 177 (1981), 479-502.
5) N. J. Korevaar, Sphere theorems via Alexandrov for constant Weingarten curvature hypersurfaces-appendix to a note of Ros, J. Differential Geom., 27 (1988), 221-223.
6) O. Kowalski, F. Tricerri and L. Vannhecke, Exemples nouveaux de variétés riemanniennes non-homogènes dont le tenseur de courbure est celui d'un espace symétrique riemannien, C. R. Acad. Sci. Paris, Sér. I, 311 (1990), 355-360.
7) O. Kowalski, F. Tricerri and L. Vanhecke, Curvature homogeneous Riemannian manifolds, J. Math. Pures Appl., to appear.
8) F. Lastaria and F. Tricerri, Curvature-orbits and locally homogeneous Riemannian manifolds, Ann. Mat. Pura Appl., to appear.
9) J. Milnor, Curvatures of left invariant metrics on Lie groups, Adv. in Math., 21 (1976), 293-329.
10) S. Montiel and A. Ros, Compact hypersurfaces: the Alexandrov theorem for higher order mean curvatures, to appear in do Carmo 60th birthday volume.
11) A. Ros, Compact hypersurfaces with constant scalar curvature and a congruence theorem, J. Differential Geom., 27 (1988), 215-220.
12) K. Sekigawa, On the Riemannian manifolds of the form B×_fF, Kodai Math. Sem. Rep., 26 (1975), 343-347.
13) I. M. Singer, Infinitesimally homogeneous spaces, Comm. Pure Appl. Math., 13 (1960), 685-697.
14) Z. I. Szabó, Classification and construction of complete hypersusfaces satisfying R(X, Y)•R=0, Acta Sci. Math., 47 (1984), 321-348.
15) Z.I. Szabó, Structure theorems on Riemannian manifolds satisfying R(X, Y)•R=0, I, Local version, J. Differential Geom., 17 (1982), 531-582.
16) Z.I. Szabó, Structure theorems on Riemannian manifolds satisfying R(X, Y)•R=0, II, Global version, Geometriae Dedicata, 19 (1985), 65-108.
17) H. Takagi, On curvature homogeneity of Riemannian manifolds, Tohoku Math. J., 26 (1974), 581-585.
18) F. Tricerri, Varietà riemanniane che hanno la stessa curvatura di uno spazio omogeneo ed una congettura di Gromov, Riv. Mat. Univ. Parma, 14 (1988), 91-104.
19) F. Tricerri and L. Vanhecke, Curvature homogeneous Riemannian manifolds, Ann. Sci. Ecole Norm. Sup., 22 (1989), 535-554.
20) T. Tsukada, Curvature homogeneous hypersurfaces immersed in a real space form, Tohoku Math. J., 40 (1988), 221-244.
21) K. Yamato, A characterization of locally homogeneous Riemann manifolds of dimension 3, Nagoga Math. J., 123 (1991), 77-90.

Right : [1] L. Bérard-Bergery, Les espaces homogènes riemanniens de dimension 4, Géométrie riemannienne en dimension 4, Séminaire A. Besse, Cedic, Paris, 1981, pp. 40-60.
[2] M. Berger, L'oeuvre d'André Lichnerowicz en géométrie riemannienne, Physique quantique et géométrie (eds. D. Bernard and Y. Choquet-Bruhat), Colloque Géométrie et Physique 1986 en l'honneur d'André Lichnerowicz, Travaux en Cours, Hermann, Paris, 1988, pp. 11-24.
[3] R. L. Bishop and B. O'Neill, Manifolds of negative curvature, Trans. Amer. Math. Soc., 145 (1969), 1-49.
[4] D. Ferus, H. Karcher and H. F. Münzner, Cliffordalgebren und neue isoparametrische Hyperflächen, Math. Z., 177 (1981), 479-502.
[5] N. J. Korevaar, Sphere theorems via Alexandrov for constant Weingarten curvature hypersurfaces-appendix to a note of Ros, J. Differential Geom., 27 (1988), 221-223.
[6] O. Kowalski, F. Tricerri and L. Vannhecke, Exemples nouveaux de variétés riemanniennes non-homogènes dont le tenseur de courbure est celui d'un espace symétrique riemannien, C. R. Acad. Sci. Paris, Sér. I, 311 (1990), 355-360.
[7] O. Kowalski, F. Tricerri and L. Vanhecke, Curvature homogeneous Riemannian manifolds, J. Math. Pures Appl., to appear.
[8] F. Lastaria and F. Tricerri, Curvature-orbits and locally homogeneous Riemannian manifolds, Ann. Mat. Pura Appl., to appear.
[9] J. Milnor, Curvatures of left invariant metrics on Lie groups, Adv. in Math., 21 (1976), 293-329.
[10] S. Montiel and A. Ros, Compact hypersurfaces: the Alexandrov theorem for higher order mean curvatures, to appear in do Carmo 60th birthday volume.
[11] A. Ros, Compact hypersurfaces with constant scalar curvature and a congruence theorem, J. Differential Geom., 27 (1988), 215-220.
[12] K. Sekigawa, On the Riemannian manifolds of the form B×_fF, Kodai Math. Sem. Rep., 26 (1975), 343-347.
[13] I. M. Singer, Infinitesimally homogeneous spaces, Comm. Pure Appl. Math., 13 (1960), 685-697.
[14] Z. I. Szabó, Classification and construction of complete hypersusfaces satisfying R(X, Y)·R=0, Acta Sci. Math., 47 (1984), 321-348.
[15] Z. I. Szabó, Structure theorems on Riemannian manifolds satisfying R(X, Y)·R=0, I, Local version, J. Differential Geom., 17 (1982), 531-582.
[16] Z. I. Szabó, Structure theorems on Riemannian manifolds satisfying R(X, Y)·R=0, II, Global version, Geometriae Dedicata, 19 (1985), 65-108.
[17] H. Takagi, On curvature homogeneity of Riemannian manifolds, Tôhoku Math. J., 26 (1974), 581-585.
[18] F. Tricerri, Varietà riemanniane che hanno la stessa curvatura di uno spazio omogeneo ed una congettura di Gromov, Riv. Mat. Univ. Parma, 14 (1988), 91-104.
[19] F. Tricerri and L. Vanhecke, Curvature homogeneous Riemannian manifolds, Ann. Sci. Ecole Norm. Sup., 22 (1989), 535-554.
[20] T. Tsukada, Curvature homogeneous hypersurfaces immersed in a real space form, Tohoku Math. J., 40 (1988), 221-244.
[21] K. Yamato, A characterization of locally homogeneous Riemann manifolds of dimension 3, Nagoga Math. J., 123 (1991), 77-90.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

Corresponding author

Correction information

Register with J-STAGE for free!