Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
Semisymmetric metric connection; almost Kenmotsu manifold; Einstein manifold; sectional curvature; Ricci tensor; Weyl conformal curvature tensor
Semisymmetric metric connection; almost Kenmotsu manifold; Einstein manifold; sectional curvature; Ricci tensor; Weyl conformal curvature tensor
Summary:
We consider a semisymmetric metric connection in an almost Kenmotsu manifold with its characteristic vector field $\xi $ belonging to the $(k,\mu )^{\prime }$-nullity distribution and $(k,\mu )$-nullity distribution respectively. We first obtain the expressions of the curvature tensor and Ricci tensor with respect to the semisymmetric metric connection in an almost Kenmotsu manifold with $\xi $ belonging to $(k,\mu )^{\prime }$- and $(k,\mu )$-nullity distribution respectively. Then we characterize an almost Kenmotsu manifold with $\xi $ belonging to $(k,\mu )^{\prime }$-nullity distribution admitting a semisymmetric metric connection.
References:
[1] Blair, D. E., Koufogiorgos, T., Papantoniou, B. J.: Contact metric manifolds satisfying a nulitty condition. Israel. J. Math. 91 (1995), 189–214. DOI 10.1007/BF02761646 | MR 1348312
[2] Blair, D. E.: Contact Manifolds in Reimannian Geometry. Lecture Notes in Mathematics 509, Springer-Verlag, Berlin, 1976.
[3] Blair, D. E.: Reimannian Geometry of Contact and Sympletic Manifolds. Progress in Mathematics 203, Birkhäuser, Basel, 2010. MR 2682326
[4] Binh, T. Q.: On Semisymmetric Connections. Periodica Mathematica Hungarica 21 (1990), 101–107. DOI 10.1007/BF01946849 | MR 1070949
[5] Barman, A.: Concirculer curvature tensor of a semi-symmetric metric connection in a Kenmotsu manifold. Thai Jornal Of Mathematics 13 (2015), 245–257. MR 3346960
[6] Barman, A.: On a special type of Remannian manifold admitting a type of semisymmetric metric connection. Novi Sad J. Math 42 (2012), 81–88. MR 3099738
[7] Barman, A.: On Para-Sasakian manifolds admitting semisymmetric metric connection. Publication de L’Insitut Mathematique 109 (2014), 239–247. DOI 10.2298/PIM1409239B | MR 3221231
[8] De, U. C., Pathok, G.: On a Semi-symmetric Metric Connection in a Kenmotsu manifold. Bull. Cal. Math. Soc. 94 (2002), 319–324. MR 1947587
[9] Dileo, G., Pastore, A. M.: Almost Kenmotsu manifolds and nullity distributions. J. Geom. 93 (2009), 46–61. DOI 10.1007/s00022-009-1974-2 | MR 2501208 | Zbl 1204.53025
[10] Dileo, G., Pastore, A. M.: Almost Kenmotsu manifolds with a condition of $\eta $-parallelsim. Differential Geom. Appl. 27 (2009), 671–679. DOI 10.1016/j.difgeo.2009.03.007 | MR 2567845
[11] Dileo, G., Pastore, A. M.: Almost Kenmotsu manifolds and local symmetri. Bull. Belg. Math. Soc. Simon Stevin 14 (2007), 343–354. MR 2341570
[12] Friedman, A., Schouten, J. A.: Über die Geometric der halbsymmetrischen Übertragung. Math., Zeitschr. 21 (1924), 211–223. DOI 10.1007/BF01187468 | MR 1544701
[13] Gray, A.: Spaces of constancy of curvature operators. Proc. Amer. Math. Soc. 17 (1966), 897–902. DOI 10.1090/S0002-9939-1966-0198392-4 | MR 0198392 | Zbl 0145.18603
[14] Hayden, H. A.: Subspace of space with torsion. Proc. London Math. Soc. 34 (1932), 27–50. DOI 10.1112/plms/s2-34.1.27 | MR 1576150
[15] Imai, T.: Notes on semi-symmetric metric conection. Tensor (N.S.) 24 (1972), 293–296. MR 0375121
[16] Kenmotsu, K.: A class of almost contact Riemannian manifolds. Tohoku Mathematical Journal 24, 1 (1972), 93–103. DOI 10.2748/tmj/1178241594 | MR 0319102 | Zbl 0245.53040
[17] Liang, Y.: On semi-symmetric recurrent-metric connection. Tensor (N.S.) 55 (1994), 107–112. MR 1310103 | Zbl 0817.53024
[18] Mishra, R. S.: Structures on Differentiable Manifold and Their Applications. Chandrama Prakasana, Allahabad, 1984.
[19] Pastore, A. M., Saltarelli, V.: Generalized nullity distribution on an almost Kenmotsu manifolds. J. Geom. 4 (2011), 168–183. MR 2929587
[20] Pastore, A. M., Saltarelli, V.: Almost Kenmotsu manifolds with conformal Reeb foliation. Bull. Belg. Math. Soc. Simon Stevin 21 (2012), 343–354. MR 2907610
[21] Pravanović, M., Pušić, N.: On manifolds admitting some semi-symmetric metric connection. Indian J. Math. 37 (1995), 37–67. MR 1366983
[22] Pušić, N.: On geodesic lines of metric semi-symmetric connection on Riemannian and hyperbolic Kählerian spaces. Novi Sad J. Math. 29 (1999), 291–299. MR 1771006
[23] Szabó, Z. I.: Structure theorems on Riemannian spaces satisfying $R(X,Y).R=0$. I. The local version. J. Differential Geom. 17, 4 (1982), 531–582. DOI 10.4310/jdg/1214437486 | MR 0683165 | Zbl 0508.53025
[24] Tanno, S.: Some differential equation on Reimannian manifolds. J. Math. Soc. Japan 30 (1978), 509–531. DOI 10.2969/jmsj/03030509 | MR 0500721
[25] Velimirović, L. S., Minčić, S. M., Stanković, M. S.: Infinitesimal deformations of curvature tensor at non-symmetric affine connection space. Mat. Vesnic 54 (2002), 219–226. MR 1996621
[26] Velimirović, L. S., Minčić, S. M., Stanković, M. S.: Infinitesimal deformations and Lie derivative of non-symmetric affine connection space. Acta Univ. Palacki. Olomuc., Fac. rer. nat., Math. 42 (2003), 111–121. MR 2056026
[27] Wang, Y., Liu, X.: On $\phi $-recurrent almost kenmotsu manifolds. Kuwait J. Sci. 42 (2015), 65–77. MR 3331380 | Zbl 1358.53040
[28] Wang, Y., Liu, X.: Second order parrallel tensors on almost Kenmotsu manifolds satisfying the nullity distributions. Filomat 28 (2014), 839–847. DOI 10.2298/FIL1404839W | MR 3360077
[29] Wang, Y., Liu, X.: Remannian semisymmetric almost Kenmotsu manifolds and nullity distributions. Ann. Polon. Math. 112 (2014), 37–46. DOI 10.4064/ap112-1-3 | MR 3244913
[30] Yano, K.: On semisymmetric metric connection. Rev. Roumaine Math. Pures Appl. 15 (1970), 1570–1586. MR 0275321
[31] Yano, K., Kon, M.: Structure on Manifolds. Series in Math. 3, World Scientific, Singapore, 1984. MR 0794310
[32] Zhao, P., Song, H.: An invariant of the projective semisymmetric connection. Chinese Quaterly J. Math. 19 (1994), 48–52.
Search
Partner of
