An explicit classification of 3-dimensional Riemannian spaces satisfying R ( X , Y ) · R = 0

Oldřich Kowalski

Czechoslovak Mathematical Journal (1996)

  • Volume: 46, Issue: 3, page 427-474
  • ISSN: 0011-4642

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Kowalski, Oldřich. "An explicit classification of 3-dimensional Riemannian spaces satisfying $R(X,Y) \cdot R = 0$." Czechoslovak Mathematical Journal 46.3 (1996): 427-474. <http://eudml.org/doc/30322>.

@article{Kowalski1996,
author = {Kowalski, Oldřich},
journal = {Czechoslovak Mathematical Journal},
keywords = {Riemannian space; symmetric space; semi-symmetric space},
language = {eng},
number = {3},
pages = {427-474},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {An explicit classification of 3-dimensional Riemannian spaces satisfying $R(X,Y) \cdot R = 0$},
url = {http://eudml.org/doc/30322},
volume = {46},
year = {1996},
}

TY - JOUR
AU - Kowalski, Oldřich
TI - An explicit classification of 3-dimensional Riemannian spaces satisfying $R(X,Y) \cdot R = 0$
JO - Czechoslovak Mathematical Journal
PY - 1996
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 46
IS - 3
SP - 427
EP - 474
LA - eng
KW - Riemannian space; symmetric space; semi-symmetric space
UR - http://eudml.org/doc/30322
ER -

References

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  13. Geodesic maps of Riemannian spaces (Russian), Publishing House “Nauka”, Moscow, 1979, pp. 256. (1979) MR0552022
  14. 10.4310/jdg/1214437486, J. Differential Geometry 17 (1982), 531–582. (1982) MR0683165DOI10.4310/jdg/1214437486
  15. Structure theorems on Riemannian manifolds satisfying R ( X , Y ) · R = 0 , II, Global version. Geometriae Dedicata (1985), 65–108. (1985) MR0797152
  16. Classification and construction of complete hypersurfaces satisfying R ( X , Y ) · R = 0 , Acta Sci. Math. 47 (1984), 321–348. (1984) MR0783309
  17. An example of Riemannian manifold satisfying R ( X , Y ) · R = 0 but not R = 0 , Tôhoku Math. J. 24 (1972), 105–108. (1972) MR0319109

Citations in EuDML Documents

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  1. Oldřich Kowalski, Masami Sekizawa, Local isometry classes of Riemannian 3 -manifolds with constant Ricci eigenvalues ρ 1 = ρ 2 ρ 3 > 0
  2. Krishnendu De, Uday Chand De, Projective Curvature Tensorin 3-dimensional Connected Trans-Sasakian Manifolds
  3. Norio Hashimoto, Masami Sekizawa, Three-dimensional conformally flat pseudo-symmetric spaces of constant type
  4. Eric Boeckx, Lieven Vanhecke, Unit tangent sphere bundles with constant scalar curvature
  5. Ülo Lumiste, Semiparallel isometric immersions of 3-dimensional semisymmetric Riemannian manifolds
  6. Ülo Lumiste, Normally flat semiparallel submanifolds in space forms as immersed semisymmetric Riemannian manifolds

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