Previous |  Up |  Next

Article

Keywords:
pseudosymmetric; Ricci-pseudosymmetric; Weyl-pseudosymmetric; $(\kappa , \mu )$-manifolds
Summary:
In this paper we classify pseudosymmetric and Ricci-pseudosymmetric $(\kappa , \mu )$-contact metric manifolds in the sense of Deszcz. Next we characterize Weyl-pseudosymmetric $(\kappa , \mu )$-contact metric manifolds.
References:
[1] Belkhelfa, M., Deszcz, R., Verstraelen, L.: Symmetry properties of Sasakian space forms. Soochow J. Math. 31 (2005), 611–616. MR 2190204 | Zbl 1087.53021
[2] Blair, D.E.: Contact manifolds in Riemannian geometry. Lecture Notes in Math., Springer–Verlag, Berlin, 1976. MR 0467588 | Zbl 0319.53026
[3] Blair, D.E., Koufogiorgos, T., Papantoniou, B.J.: Contact metric manifolds satisfying a nullity condition. Israel J. Math. 91 (1995), 57–65. DOI 10.1007/BF02761646 | MR 1348312 | Zbl 0837.53038
[4] Calvaruso, G.: Conformally flat pseudo–symmetric spaces of constant type. Czechoslovak Math. J. 56 (2006), 649–657. DOI 10.1007/s10587-006-0045-1 | MR 2291764 | Zbl 1164.53339
[5] Chaki, M.C., Chaki, B.: On pseudosymmetric manifolds admitting a type of semisymmetric connection. Soochow J. Math. 13 (1987), 1–7. MR 0924340
[6] Cho, J.T., Inoguchi, J.-I.: Pseudo–symmetric contact 3–manifolds. J. Korean Math. Soc. 42 (2005), 913–932. DOI 10.4134/JKMS.2005.42.5.913 | MR 2157352 | Zbl 1081.53018
[7] Cho, J.T., Inoguchi, J.–I., Lee, J.–E.: Pseudo–symmetric contact 3–manifolds. III. Colloq. Math. 114 (2009), 77–98. DOI 10.4064/cm114-1-7 | MR 2457280 | Zbl 1163.53017
[8] Defever, F., Deszcz, R., Verstraelen, L.: On pseudosymmetric para–Kähler manifolds. Colloq. Math. 74 (1997), 253–260. DOI 10.4064/cm-74-2-253-260 | MR 1477567 | Zbl 0903.53025
[9] Defever, F., Deszcz, R., Verstraelen, L., Vrancken, L.: On pseudosymmetric spacetimes. J. Math. Phys. 35 (1994), 5908–5921. DOI 10.1063/1.530718 | MR 1299927
[10] Deszcz, R.: On Ricci–pseudo–symmetric warped products. Demonstratio Math. 22 (1989), 1053–1065. MR 1077121 | Zbl 0707.53020
[11] Deszcz, R.: On pseudosymmetric spaces. Bull. Soc. Math. Belg. Sér. A 44 (1992), 1–34. MR 1315367 | Zbl 0808.53012
[12] Gouli-Andreou, F., Moutafi, E.: Two classes of pseudosymmetric contact metric 3–manifolds. Pacific J. Math. 239 (2009), 17–37. DOI 10.2140/pjm.2009.239.17 | MR 2449009 | Zbl 1155.53045
[13] Gouli–Andreou, F., Moutafi, E.: Three classes of pseudosymmetric contact metric 3–manifolds. Pacific J. Math. 245 (2010), 57–77. DOI 10.2140/pjm.2010.245.57 | MR 2602682 | Zbl 1186.53043
[14] Hashimoto, N., Sekizawa, M.: Three-dimensional conformally flat pseudo–symmetric spaces of constant type. Arch. Math. (Brno) 36 (2000), 279–286. MR 1811172 | Zbl 1054.53060
[15] Kowalski, O., Sekizawa, M.: Local isometry classes of Riemannian 3–manifolds with constant Ricci eigenvalues $\rho _1 = \rho _ 2\ne \rho _ 3$. Arch. Math. (Brno) 32 (1996), 137–145. MR 1407345
[16] Kowalski, O., Sekizawa, M.: Three–dimensional Riemannian manifolds of c–conullity two. World Scientific (Singapore–New Jersey–London–Hong Kong) (1996), Published as Chapter 11 in Monograph E. Boeckx, O. Kowalski, L. Vanhecke, Riemannian Manifolds of Conullity Two.
[17] Kowalski, O., Sekizawa, M.: Pseudo–symmetric spaces of constant type in dimension three–elliptic spaces. Rend. Mat. Appl. (7) 17 (1997), 477–512. MR 1608724 | Zbl 0889.53026
[18] Kowalski, O., Sekizawa, M.: Pseudo–symmetric spaces of constant type in dimension three–non–elliptic spaces. Bull. Tokyo Gakugei Univ. (4) 50 (1998), 1–28. MR 1656076 | Zbl 0945.53020
[19] Ogiue, K.: On almost contact manifolds admitting axiom of planes or axiom of free mobility. Kodai Math. Sem. Rep. 16 (1964), 223–232. DOI 10.2996/kmj/1138844949 | MR 0172223 | Zbl 0136.18003
[20] O’Neill, B.: Semi–Riemannian Geometry. Academic Press New York, 1983. MR 0719023 | Zbl 0531.53051
[21] Özgür, C.: On Kenmotsu manifolds satisfying certain pseudosymmetric conditions. World Appl. Sci. J. 1 (2006), 144–149.
[22] Papantoniou, B.J.: Contact Riemannian manifolds satifying $R(\xi , X)\cdot R = 0$ and $ \xi \in (\kappa , \mu )$–nullity distribution. Yokohama Math. J. 40 (1993), 149–161. MR 1216349
[23] Prakasha, D.G., Bagewadi, C.S., Basavarajappa, N.S.: On pseudosymmetric Lorentzian $\alpha $–Sasakian manifolds. Int. J. Pure Appl. Math. 48 (2008), 57–65. MR 2456434 | Zbl 1155.53019
[24] Szabó, Z.I.: Structure theorems on Riemannian manifolds satisfying $R(X,Y)\cdot R=0$. I. The local version. J. Differential Geom. 17 (1982), 531–582. DOI 10.4310/jdg/1214437486 | MR 0683165
[25] Szabó, Z.I.: Structure theorems on Riemannian manifolds satisfying $R(X,Y)\cdot R=0$. II. Global versions. Geom. Dedicata 19 (1) (1985), 65–108. DOI 10.1007/BF00233102 | MR 0797152
[26] Tanno, S.: Ricci curvatures of contact Riemannian manifolds. Tohoku Math. J. 40 (1988), 441–448. DOI 10.2748/tmj/1178227985 | MR 0957055 | Zbl 0655.53035
Partner of
EuDML logo