Volume 34 | Number 2 | Year 2016 | Article Id. IJMTT-V34P520 | DOI : https://doi.org/10.14445/22315373/IJMTT-V34P520
The present paper deals with the study of pseudo Ricci-symmetric contact metric manifold. Here we consider generalized pseudo- Ricci symmetric, almost pseudo Ricci-symmetric and -pseudo Ricci-symmetric contact metric manifold and obtained some interesting results.
[1]. K. Arslan, R. Ezentas, C. Murathan and C. Ozgur, On pseudo Ricci symmetric manifolds, Balkan J.Geom. and Appl., 6 (2001), 1-5.
[2]. D.E. Blair, Contact manifolds in Riemannian geometry. Lecture Notes in Math., No. 509, Springer, 1976.
[3]. D.E. Blair, Two remarks on contact metric structures., Tohoku Math. J., 29 (1977), 319-324.
[4]. D.E. Blair, J.S. Kim and M.M. Tripathi, On the concircular curvature tensor of a contact metric manifold, J. Korean Math. Soc., 42 (2005), 883-892.
[5]. D.E. Blair, T. Koufogiorgos and Papantoniou, Contact metric manifolds satisfying a nullity condition, Israel J. Math., 91, 189 (1995).
[6]. E. Boeckx, A full classification of contact metric (k, μ)- spaces, Illinois J. Math., 44 (1), 212 (2000).
[7]. W.M. Boothby and H.C. Wang, On contact manifolds, Ann. of Math., 68 (1958), 721-734.
[8]. E. Cartan, Sur une classe remarquable d’espaces de Riemannian, Bull. Soc. Math. France, 54 (1926), 214-264.
[9]. M.C. Chaki, On pseudo-symmetric manifolds, An. Sti. Ale Univ., AL. I. CUZA” Din Iasi, 33 (1987), 53-58.
[10]. M.C. Chaki, On pseudo Ricci symmetric manifolds, Bulg. J. Phys., 15 (1988), 526-531.
[11]. M.C. Chaki and T. Kawaguchi, On almost pseudo Ricci symmetric man- ifolds, Tensor N. S., 68 (2007),10-14.
[12]. R. Deszcz, On pseudosymmetric spaces, Bull. Soc. Math. Belg. Ser. A, 44 (1) (1992), 1-34.
[13]. R. Deszcz, On Ricci-pseudosymmetric warped products, Demonstratio Math., 22 (1989), 1053-1065.
[14]. U.C. De and B.K. Mazumder, On pseudo Ricci symmetric spaces, Tensor N. S., 60 (1998), 135-138.
[15]. U.C. De, C. Murathan and C. Ozgur, Pseudo symmetric and pseudo Ricci symmetric warped product manifolds, Commun. Korean Math. Soc., 25 (2010), 615-621.
[16]. Erdal Ozusaglam, On special weakly Ricci-symmetric Smanifold, International Journal of Geometry, 2(1) (2013), 75-78.
[17]. C. Ozgur, On weak symmetries of Lorentzian para-Sasakian manifolds, Rad. Mat., 11 (2) (2002), 263-270.
[18]. E.M. Patterson, Some theorems on Ricci-recurrent spaces, J. London Math. Soc., 27 (1952), 287-295.
[19]. H. Singh and Q. Khan, On special weakly symmetric Riemannian manifolds, Publ. Math. Debrecen, Hungary, 58 (2001), 523-536.
[20]. G.T. Sreenivasa, Venkatesha, C.S.Bagewadi and K. Naganagoud, On weakly symmetric and special weakly Ricci-symmetric Lorentzian -Kenmotsu manifolds, Acta Universitatis Apulensis, 19 (2009), 47-54.
[21]. Z.I. Szabo, Structure theorems on Riemannian space satisfying R(X, Y ).R = 0, I, The local version, J. Differential Geom., 17, 531 (1982).
[22]. S. Shukla and M.K. Shukla, On -Ricci symmetric Kenmotsu manifolds, Novi Sad J. Math., 39 (2), (2009), 89- 95.
[23]. L. Tamssy and T. Binh, On weakly symmetric and weakly projective symmetric Riemannian manifolds, Dierential geometry and its applications, Colloq. Math. Soc. Jnos Bolyai, Amsterdam, 1992, 663-670.
[24]. S. Tanno, Ricci curvatures of contact Riemannian manifolds, Tohoku Mathematical journal, 40, 441(1988).
[25]. A.G. Walker, On Ruses spaces of recurrent curvature, Proc. London Math. Soc., 52 (1950), 36-64.
[26]. K. Yano and M. Kon, Structures on Manifolds, Vol. 3 of Series in Pure Mathematics, World Scientific, Singapore, (1984).
R.T. Naveen Kumar, Venkatesha, "On Pseudo Ricci-Symmetric N(k) - Contact Metric Manifold," International Journal of Mathematics Trends and Technology (IJMTT), vol. 34, no. 2, pp. 118-121, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V34P520