| Title:
|
An explicit classification of 3-dimensional Riemannian spaces satisfying $R(X,Y) \cdot R = 0$ (English) |
| Author:
|
Kowalski, Oldřich |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
46 |
| Issue:
|
3 |
| Year:
|
1996 |
| Pages:
|
427-474 |
| . |
| Category:
|
math |
| . |
| MSC:
|
53B20 |
| MSC:
|
53C20 |
| MSC:
|
53C25 |
| idZBL:
|
Zbl 0879.53014 |
| idMR:
|
MR1408298 |
| DOI:
|
10.21136/CMJ.1996.127308 |
| . |
| Date available:
|
2009-09-24T09:58:40Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127308 |
| . |
| Reference:
|
[BKV] E. Boeckx, O. Kowalski and L. Vanhecke: Nonhomogeneous relatives of symmetric spaces.Differential Geometry and its Applications 4 (1994), 45–69. MR 1264908 |
| Reference:
|
[Ca 1] E. Cartan: Leçons sur la géométrie des espaces de Riemann. 2nd edition.Paris, 1946. MR 0020842 |
| Reference:
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[Ca 2] E. Cartan: Les systèmes différentiels extérieurs et leurs applications géométriques.Hermann, Paris, 1945. Zbl 0063.00734, MR 0016174 |
| Reference:
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[K] O. Kowalski: Riemannian 3-manifolds with constant Ricci roots $\rho_1 = \rho_2 \neq \rho_3$.Nagoya Math. J. 132 (1993), 1–36. MR 1253692 |
| Reference:
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[KN] S. Kobayashi and K. Nomizu: Foundations of differential geometry.vol. I, Interscience Publishers, New York London, 1963. MR 0152974 |
| Reference:
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[KTV 1] O. Kowalski, F. Tricerri and L. Vanhecke: New examples of nonhomogeneous Riemannian manifolds whose curvature tensor is that of a Riemannian symmetric space.C.R. Acad. Sci. Paris, Série I, 311 (1990), 355–360. MR 1071643 |
| Reference:
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[KTV 2] O. Kowalski, F. Tricerri and L. Vanhecke: Curvature homogeneous Riemannian manifolds.J. Math. Pures et Appl. 71 (1992), 471–501. MR 1193605 |
| Reference:
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[KTV 3] O. Kowalski, F. Tricerri and L. Vanhecke: Curvature homogeneous spaces with a solvable Lie group as homogeneous model.J. Math. Soc. Japan 44 (1992), 461–484. MR 1167378, 10.2969/jmsj/04430461 |
| Reference:
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[Lu] Ü. Lumiste: Semi-symmetric submanifold as the second order envelope of symmetric submanifolds.Proc. Estonian Acad. Sci. Phys. Math. No1 35 (1990), 1–8. Zbl 0704.53017 |
| Reference:
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[N] K. Nomizu: On hypersurfaces satisfying a certain condition on the curvature tensor.Tôhoku Math. J. 20 (1968), 46–59. Zbl 0174.53301, MR 0226549, 10.2748/tmj/1178243217 |
| Reference:
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[Se] K. Sekigawa: On the Riemannian manifolds of the form $B \times _fF$.Kodai Math. Sem. Rep. 26 (1975), 343–347. MR 0438253, 10.2996/kmj/1138847016 |
| Reference:
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[Si 1] N.S. Sinjukov: On geodesic maps of Riemannian spaces (Russian).Trudy Vsesojuz, Matem. Sjezda (1956), 167–168. |
| Reference:
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[Si 2] N.S. Sinjukov: Geodesic maps of Riemannian spaces (Russian).Publishing House “Nauka”, Moscow, 1979, pp. 256. MR 0552022 |
| Reference:
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[Sz 1] Z.I. Szabó: Structure theorems on Riemannian manifolds satisfying $R(X,Y) \cdot R = 0$, I, Local version.J. Differential Geometry 17 (1982), 531–582. MR 0683165, 10.4310/jdg/1214437486 |
| Reference:
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[Sz 2] Z.I. Szabó: Structure theorems on Riemannian manifolds satisfying $R(X,Y) \cdot R = 0$.II, Global version. Geometriae Dedicata (1985), 65–108. MR 0797152 |
| Reference:
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[Sz 3] Z.I. Szabó: Classification and construction of complete hypersurfaces satisfying $R(X,Y) \cdot R = 0$.Acta Sci. Math. 47 (1984), 321–348. MR 0783309 |
| Reference:
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[T] H. Takagi: An example of Riemannian manifold satisfying $R(X,Y) \cdot R = 0$ but not $\nabla R = 0$.Tôhoku Math. J. 24 (1972), 105–108. MR 0319109 |
| . |
