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1991 | 62 | 1 | 103-120
Tytuł artykułu

On four-dimensional Riemannian warped product manifolds satisfying certain pseudo-symmetry curvature conditions

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Rocznik
Tom
62
Numer
1
Strony
103-120
Opis fizyczny
Daty
wydano
1991
otrzymano
1989-03-21
poprawiono
1990-03-09
Twórcy
  • Department of Mathematics, Agricultural Academy, C. Norwida 25, 50-375 Wrocław, Poland
Bibliografia
  • [1] R. L. Bishop and B. O'Neill, Manifolds of negative curvature, Trans. Amer. Math. Soc. 145 (1969), 1-49.
  • [2] J. Deprez, R. Deszcz and L. Verstraelen, Examples of pseudo-symmetric conformally flat warped products, Chinese J. Math. 17 (1989), 51-65.
  • [3] J. Deprez, R. Deszcz and L. Verstraelen, Pseudo-symmetry curvature conditions on hypersurfaces of Euclidean spaces and on Kählerian manifolds, Ann. Fac. Sci. Univ. Paul Sabatier Toulouse 9 (1988), 183-192.
  • [4] J. Deprez, P. Verheyen and L. Verstraelen, Characterization of conformally flat hypersurfaces, Czechoslovak Math. J. 35 (110) (1985), 140-145.
  • [5] A. Derdziński, Exemples de métriques de Kaehler et d'Einstein autoduales sur le plan complexe, in: Géométrie riemannienne en dimension 4 (Séminaire Arthur Besse 1978/79), Cedic/Fernand Nathan, Paris 1981, 334-346.
  • [6] R. Deszcz, On pseudo-symmetric warped product manifolds, to appear.
  • [7] R. Deszcz, On Ricci-pseudo-symmetric warped products, Demonstratio Math. 22 (1989), 1053-1065.
  • [8] R. Deszcz, On pseudo-symmetric totally umbilical submanifolds of Riemannian manifolds admitting some types of generalized curvature tensors, Zeszyty Naukowe Politech. Śląsk., in print.
  • [9] R. Deszcz, On conformally flat Riemannian manifolds satisfying certain curvature conditions, Tensor (N.S.), in print.
  • [10] R. Deszcz, Examples of four-dimensional Riemannian manifolds satisfying some pseudo-symmetry curvature conditions, in: Geometry and Topology of Submanifolds, II, Avignon, May 1988, World Sci. Publ., Singapore 1990, 134-143.
  • [11] R. Deszcz and W. Grycak, On some class of warped product manifolds, Bull. Inst. Math. Acad. Sinica 15 (1987), 311-322.
  • [12] R. Deszcz and W. Grycak, On manifolds satisfying some curvature conditions, Colloq. Math. 57 (1989), 89-92.
  • [13] R. Deszcz and W. Grycak, On certain curvature conditions on Riemannian manifolds, ibid. 58 (1990), 259-268.
  • [14] R. Deszcz and M. Hotloś, Remarks on Riemannian manifolds satisfying certain curvature condition imposed on the Ricci tensor, Prace Nauk. Politech. Szczec. 11 (1989), 23-34.
  • [15] L. P. Eisenhart, Riemannian Geometry, Princeton Univ. Press, Princeton 1966.
  • [16] W. Grycak, Riemannian manifolds with a symmetry condition imposed on the $2$-nd derivative of the conformal curvature tensor, Tensor (N.S.) 46 (1987), 287-290.
  • [17] G. I. Kruchkovich, On semi-reducible Riemannian spaces, Dokl. Akad. Nauk SSSR 115 (1957), 862-865 (in Russian).
  • [18] K. Nomizu, On the decomposition of generalized curvature tensor fields, in: Differential Geometry in honor of K. Yano, Kinokuniya, Tokyo 1972, 335-345.
  • [19] Y. Ogawa, On conformally flat spaces with warped product Riemannian metric, Nat. Sci. Rep. Ochanomizu Univ. 29 (1978), 117-127.
  • [20] Z. I. Szabó, Structure theorems on Riemannian spaces satisfying $R(X,Y)· R=0$, J. Differential Geom. 17 (1982), 531-582.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv62i1p103bwm
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