Remarks On Four-Dimensional PseudosymmetricKahlerian Manifolds

Beldjilali Gherici*, Mohamed Belkhelfa**, Hasni Abdelbasset***
*-**-*** Laboratoire de Physique Quantique de la matière et de Modélisation Math_ematique, (LPQ3M), Université de Mascara, Mascara, Algeria.
Periodicity:October - December'2013
DOI : https://doi.org/10.26634/jmat.2.4.2609

Abstract

In the present paper, we prove that for a 4-dimensional properly pseudosymmetric Kählerian manifold M, the Ricci tensor vanishes on the set p Î {M/ f(p) 6≠ 0} where f is the structure fonction (i.e R(X,Y ) = f(XÙY).R) and for f > 0 the manifold is not compact. Various examples are discussed.

Keywords

Four-dimensional Pseudosymmetric Kahlerian Manifolds, Ricci tensor.

How to Cite this Article?

Gherici, B., Mohamed, B., and Abdelbasset, H. (2013). Remarks on Four-Dimensional Pseudosymmetric Kahlerian Manifolds. i-manager’s Journal on Mathematics, 2(4), 1-6. https://doi.org/10.26634/jmat.2.4.2609

References

[1]. Beldjilali, G. (january,2012). La pseudosym_etrie holomorphique, Mémoire de Magister, Université de Mascara, Algérie.
[2]. Belkhelfa, M. & Hasni, A. (2011). Symmetric propreties of Thurston geometry F4, Proceedings of the Conference RIGA 2011, Mihai, Adela (ed.) et al., Riemannian Geometry and Applications, Bucharest, Romania, 29{40.
[3]. Defever, F., Deszcz, R., & Verstraelen, L. (1997). On pseudo-symmetric para-Kahler manifolds, Colloq. Math, 74 ,253{260.
[4]. Eisenhart L.P. (1997). Riemannian geometry, Princeton University Press, Princeton, NJ.
[5]. Haesen, S., & Verstraelen, L. (2009). Natural Intrinsic Geometrical Symmetries, Symmetry, Integrability and Geometry: Methods and Applications, SIGMA 5 , 086,15 pages.
[6]. Jelonek, W. (2009). Compact holomorphically pseudosymmetric Kählerian manifolds, Colloq. Math.; 117, 243-249.
[7]. Olszak, Z. (1989). Bochner at Kählerian manifolds with certain condition on the Ricci tensor, Simon Stevin, 63 , 295-303.
[8]. Olszak, Z. (2003). On the existence of pseudo-symmetric Kählerian manifolds, Colloq. Math, 95 , 185-189.
[9]. Olszak, Z. (2009). On compact holomorphically pseudosymmetric Kähler manifolds, Cent. Eur. J. Math., 7 , No. 3, 442- 451.
[10]. Olszak, Z. (Priprint). Weyl-pseudosymmetric and Bochner-pseudosymmetric Kählerian manifolds of dimension 4, Preprint.
[11]. Tachibana, S. (1974). A theorem on Riemannian manifolds of positive curvature operator. Proc. Jpn. Acad. Ser. Math. Sci. 50, 301-302.
If you have access to this article please login to view the article or kindly login to purchase the article

Purchase Instant Access

Single Article

North Americas,UK,
Middle East,Europe
India Rest of world
USD EUR INR USD-ROW
Pdf 35 35 200 20
Online 35 35 200 15
Pdf & Online 35 35 400 25

Options for accessing this content:
  • If you would like institutional access to this content, please recommend the title to your librarian.
    Library Recommendation Form
  • If you already have i-manager's user account: Login above and proceed to purchase the article.
  • New Users: Please register, then proceed to purchase the article.