Curvature properties of some four-dimensional manifolds

• Autorzy: Głogowska, M.
• Języki publikacji: EN

Abstrakty

EN

We present curvature properties of four-dimensional semi-Riemannian metrics related to semi-integrable almost Grassmann structures studied by M.A. Akivis and V.V. Goldberg in [2j.

Słowa kluczowe

EN

warped product; pseudosymmetry type manifold; Bach tensor; Grassmann structure

• Czasopismo: Demonstratio Mathematica
• Rocznik: 2001
• Tom: Vol. 34, nr 4
• Strony: 901-918
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Głogowska, M.

• Department of Mathematics Agricultural University of Wrocław ul. Grunwaldzka 53 PL-50-357 Wrocław, Poland,

Bibliografia

• [1] M. A. Akivis and V. V. Goldberg, Conformai Differential Geometry and its Generalizations, Wiley-Interscience Publication, New York, 1996.
• [2] M. A. Akivis and V. V. Goldberg, Semiintegrable almost Grassmann structures, Differential Geom. Appl. 10 (1999), 257-294.
• [3] A. L. Besse, Einstein Manifolds, Springer-Verlag, Berlin, Heidelberg, New York, 1987.
• [4] F. Defever, R. Deszcz, M. Głogowska, V. V. Goldberg, and L. Verstraelen, A class of four-dimensional warped products, Dept. Math., Agricultural Univ. Wrocław, Ser. A, Theory and Methods, Report No. 65, 1998.
• [5] R. Deszcz, On four-dimensional Riemannian warped product manifolds satisfying certain pseudo-symmetry curvature conditions, Colloq. Math. 62 (1991), 103-120.
• [6] R. Deszcz, On pseudosymmetric spaces, Bull. Soc. Math. Belg. 44 (1992), Sér. A, 1-34.
• [7] R. Deszcz, M. Głogowska, M. Hotloś, D. Kowalczyk, and L. Verstraelen, A review on pseudosymmetry type manifolds, Dept. Math., Agricultural Univ. Wrocław, Ser. A, Theory and Methods, Report No. 84, 2000.
• [8] R. Deszcz, M. Głogowska, M. Hotloś, and Z. Sentürk, On certain quasi-Einstein semisymmetric hypersurfaces, Annales Univ. Sci. Budapest. 41 (1998), 151-164.
• [9] R. Deszcz and M. Hotloś, On a certain extension of the class of semisymmetric manifolds, Publ. Inst. Math. (Beograd) (N.S.) 63 (77) (1998), 115-130.
• [10] R. Deszcz and M. Hotloś, On a certain subclass of pseudosymmetric manifolds, Publ. Math. Debrecen 53 (1998), 29-48.
• [11] R. Deszcz and M. Kucharski, On a certain curvature property of generalized Robertson-Walker spacetimes, Tsukuba J. Math. 23 (1999), 113-130.
• [12] M. Głogowska, On some class of semisymmetric manifolds, Dept. Math., Agricultural Univ. Wrocław, Ser. A, Theory and Methods, Report No. 73, 1999.
• [13] E. M. Patterson, A class of critical Riemannian metrics, J. London Math. Soc. 23 (1981), 349-358.
• [14] R. Schimming, On the Bach and the Bach-Einstein gravitational fiel equations, in: Proc. Int. Sem. Current topics in Mathematical Cosmology, Potsdam, Germany, 1998, World Sci. Publishing, 1998, 39-46.
• [15] Z. I. Szabo, Structure theorems on Riemannian spaces satisfying R(X, Y) • R = 0, I. The local version, J. Diff. Geom. 17 (1982), 531-582.
• [16] L. Yerstraelen, Comments on pseudo-symmetry in the sense of Ryszard Deszcz, in: Geometry and Topology of Submanifolds, VI, World Sci. Publishing, River Edge, NJ, 1994, 199-209.