On Bochner semisymmetric para-Kahlerian manifolds

• Autorzy: Łuczyszyn D.
• Języki publikacji: EN

Abstrakty

EN

A semisymmetric (R'R = 0) para-Kahlerian manifold is obviously Bochner semisymmetric (R' B = 0). In the present paper, we prove the following partially inverse theorem: If a para-Kahlerian manifold is Bochner semisymmetric and the Bochner curvature tensor B does not vanish at each point of the manifold, then the manifold is semisymmetric. Moreover, we establish new examples of para-Kahlerian manifolds which are: (1) semisymmetric and not Bochner flat; (2) Bochner flat and not semisymmetric.

Słowa kluczowe

EN

Bochner semisymetric manifold; Para-Kahlerian manifold; semisymmetric manifold

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2001
• Tom: Vol. 34, nr 4
• Strony: 933--942
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Łuczyszyn D.

• Institute of Mathematics Wrocław University of Technology Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland

Bibliografia

• [1] C. L. Bejan, The Bochner curvature tensor on a hyperbolic Kahler manifold, In: Colloquia Mathematica Societatis Jànos Bolyai, 56. Differential Geometry, Eger (Hungary), 1989, pp. 93-99.
• [2] E. Boeckx, O. Kowalski and L. Vanhecke, Riemannian Manifolds of Conullity Two, World Scientific Publishing Co., Singapore, 1996.
• [3] A. Bonome, R. Castro, E. García-Río, L. Hervella and R. Vázquez-Lorenzo, On the paraholomorphic sectional curvature of almost para-Hermitian manifolds, Houston J. Math. 24 (1998), 277-300.
• [4] V. Cruceanu, P. Fortuny and P. M. Gadea, A survey on paracomplex geometry, Rocky Mountain J. Math. 26, 1996, 83-115.
• [5] V. Cruceanu, P. M. Gadea and J. Munôz Masqué, Para-Hermitian and para-Kàhler manifolds, Quaderni Inst. Mat., Fac. Economía, Univ. Messina 1, 1995, 72pp.
• [6] F. Defever, R. Deszcz and L. Verstraelen, On semisymmetric para-Kàhler manifolds, Acta Math. Hungarica 74 (1997), 7-17.
• [7] F. Defever, R. Deszcz and L. Verstraelen, On pseudosymmetric para-Kàhler manifolds, Colloq. Math. 74 (1997), 253-260.
• [8] E. García-Río, L. Hervella and R. Vázquez-Lorenzo, Curvature properties of para-Kàhler manifolds, In: New developments in differential geometry (Debrecen, 1994), pp. 193-200, Math. Appl. 350, Kluwer Acad. Publ., Dordrecht, 1996.
• [9] M. Hotlos, On a certain class of Kàhlerian manifolds, Demonstratio Math. 12 (1979), 935-945.
• [10] D. Luczyszyn, On para-Kàhlerian manifolds with recurrent paraholomorphic projective curvature, Math. Balkanica, in print.
• [11] N. Pusic, On an invariant tensor of a conformai transformation of a hyperbolic Kaehlerian manifold, Zb. Rad. Fil. Fak. Nis, Ser. Mat. 4 (1990), 55-64.
• [12] N. Pusic, On HB-recurrent hyperbolic Kaehlerian spaces, Publ. Inst. Math. (Beograd) N.S. 55 (69) (1994), 64-74.
• [13] N. Pusic, On HB-flat hyperbolic Kaehlerian spaces, Mat. Vesnik 49 (1997), 35-44.
• [14] N. S. Sinjukov, Geodesic Maps of Riernannian Spaces, (in Russian), Publishing House "Nauka", Moscow, 1979.
• [15] Z. I. Szabo, Structure theorems on Riernannian manifolds satisfying R(X,Y)R=0, I, Local version; II, Global versions, J. Diff. Geom. 17 (1982), 531-582; Geom. Dedicata 19 (1985), 65-108.