Certain curvature characterizations of affine hypersurfaces

Ryszard Deszcz

Colloquium Mathematicae (1992)

  • Volume: 63, Issue: 1, page 21-39
  • ISSN: 0010-1354

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Deszcz, Ryszard. "Certain curvature characterizations of affine hypersurfaces." Colloquium Mathematicae 63.1 (1992): 21-39. <http://eudml.org/doc/210131>.

@article{Deszcz1992,
author = {Deszcz, Ryszard},
journal = {Colloquium Mathematicae},
keywords = {pseudo-symmetric spaces; equiaffine Einstein metrics; quasiumbilical hypersurfaces; affine sphere},
language = {eng},
number = {1},
pages = {21-39},
title = {Certain curvature characterizations of affine hypersurfaces},
url = {http://eudml.org/doc/210131},
volume = {63},
year = {1992},
}

TY - JOUR
AU - Deszcz, Ryszard
TI - Certain curvature characterizations of affine hypersurfaces
JO - Colloquium Mathematicae
PY - 1992
VL - 63
IS - 1
SP - 21
EP - 39
LA - eng
KW - pseudo-symmetric spaces; equiaffine Einstein metrics; quasiumbilical hypersurfaces; affine sphere
UR - http://eudml.org/doc/210131
ER -

References

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  3. [3] J. Deprez, R. Deszcz and L. Verstraelen, Pseudosymmetry curvature conditions on hypersurfaces of Euclidean spaces and on Kählerian manifolds, Ann. Fac. Sci. Toulouse 9 (1988), 183-192. Zbl0668.53010
  4. [4] J. Deprez, R. Deszcz and L. Verstraelen, Examples of pseudosymmetric conformally flat warped products, Chinese J. Math. 17 (1989), 51-65. Zbl0678.53022
  5. [5] R. Deszcz, Notes on totally umbilical submanifolds, in: Geometry and Topology of Submanifolds, Proc. Luminy, May 1987, World Sci., Singapore 1989, 89-97. Zbl0735.53042
  6. [6] R. Deszcz, On Ricci-pseudosymmetric warped products, Demonstratio Math. 22 (1989), 1053-1065. Zbl0707.53020
  7. [7] R. Deszcz, Examples of four dimensional Riemannian manifolds satisfying some pseudosymmetry curvature condition, in: Differential Geometry and its Applications, II, Proc. Avignon, May/June 1988, World Sci., Singapore 1990, 134-143. 
  8. [8] R. Deszcz, On conformally flat Riemannian manifolds satisfying certain curvature conditions, Tensor (N.S.) 49 (1990), 134-145. Zbl0742.53006
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  10. [10] R. Deszcz, On pseudosymmetric warped product manifolds, J. Geom., to appear. Zbl0843.53011
  11. [11] R. Deszcz, On pseudosymmetric totally umbilical submanifolds of Riemannian manifolds admitting some types of generalized curvature tensors, Zeszyty Nauk. Politech. Śląsk., in print. 
  12. [12] R. Deszcz and W. Grycak, On some class of warped product manifolds, Bull. Inst. Math. Acad. Sinica 19 (1987), 271-282. Zbl0633.53031
  13. [13] R. Deszcz and W. Grycak, On manifolds satisfying some curvature conditions, Colloq. Math. 57 (1989), 89-92. Zbl0698.53011
  14. [14] R. Deszcz and W. Grycak, On certain curvature conditions on Riemannian manifolds, ibid. 58 (1990), 259-268. Zbl0707.53019
  15. [15] R. Deszcz and M. Hotloś, On geodesic mappings in pseudosymmetric manifolds, Bull. Inst. Math. Acad. Sinica 16 (1988), 251-262. Zbl0668.53007
  16. [16] R. Deszcz and M. Hotloś, Notes on pseudosymmetric manifolds admitting special geodesic mappings, Soochow J. Math. 15 (1989), 19-27. Zbl0696.53014
  17. [17] R. Deszcz and M. Hotloś, Remarks on Riemannian manifolds satisfying certain curvature condition imposed on the Ricci tensor, Prace Nauk. Politech. Szczec. 11 (1988), 23-34. Zbl0744.53008
  18. [18] R. Deszcz and M. Hotloś, On conformally related four-dimensional pseudosymmetric metrics, Rend. Sem. Fac. Univ. Cagliari 59 (1989), 165-175. Zbl0791.53022
  19. [19] R. Deszcz and M. Hotloś, On conformally related pseudosymmetric metrics, ibid., to appear. Zbl0852.53015
  20. [20] R. Deszcz, L. Verstraelen and L. Vrancken, On the symmetry of warped product spacetimes, Gen. Rel. Gravit. 23 (1991), 671-681. Zbl0723.53009
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  22. [22] K. Nomizu, What is affine differential geometry?, in: Proc. Differential Geom., Münster 1982, 42-43. 
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  25. [25] Z. Olszak, Bochner flat Kählerian manifolds with certain condition on the Ricci tensor, Simon Stevin 63 (1989), 295-303. Zbl0629.53059
  26. [26] B. Opozda, New affine curvature tensor and its properties, lecture given during the meeting 'Current Topics in Affine Differential Geometry', Leuven 1989. 
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  28. [28] U. Simon, Hypersurfaces in equiaffine differential geometry, Geom. Dedicata 17 (1984), 157-168. Zbl0553.53004
  29. [29] U. Simon, The fundamental theorem in affine hypersurface theory, ibid. 26 (1988), 125-137. Zbl0641.53011
  30. [30] P. Verheyen, Hyperoppervlakken in een affiene ruimte, Ph.D. thesis, Katholieke Universiteit Leuven, 1983. 
  31. [31] P. Verheyen and L. Verstraelen, Locally symmetric affine hypersurfaces, Proc. Amer. Math. Soc. 93 (1985), 101-105. Zbl0535.53007

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