Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
Quarter-symmetric metric connection; Lorentzian $\alpha $-Sasakian manifold; locally $\phi $-symmetric manifold; locally projective $\phi $-symmetric manifold; $\xi $-projectively flat Lorentzian $\alpha $-Sasakian manifold
Quarter-symmetric metric connection; Lorentzian $\alpha $-Sasakian manifold; locally $\phi $-symmetric manifold; locally projective $\phi $-symmetric manifold; $\xi $-projectively flat Lorentzian $\alpha $-Sasakian manifold
Summary:
The object of the present paper is to study a quarter-symmetric metric connection in an Lorentzian $\alpha $-Sasakian manifold. We study some curvature properties of an Lorentzian $\alpha $-Sasakian manifold with respect to the quarter-symmetric metric connection. We study locally $\phi $-symmetric, $\phi $-symmetric, locally projective $\phi $-symmetric, $\xi $-projectively flat Lorentzian $\alpha $-Sasakian manifold with respect to the quarter-symmetric metric connection.
References:
[1] Bagewadi, C. S., Prakasha, D. G., Venkatesha, A.: A Study of Ricci quarter-symmetric metric connection on a Riemannian manifold. Indian J. Math. 50, 3 (2008), 607–615. MR 2483702 | Zbl 1159.53323
[2] Boeckx, E., Buecken, P., Vanhecke, L.: $\phi $-symmetric contact metric spaces. Glasgow Math. J. 41 (1999), 409–416. DOI 10.1017/S0017089599000579 | MR 1720426
[3] Formella, S., Mikeš, J.: Geodesic mappings of Einstein spaces. Ann. Sci. Stetinenses 9 (1994), 31–40.
[4] Friedmann, A., Schouten, J. A.: Uber die Geometrie der halbsymmetrischen Uber-tragung. Math. Zeitschr 21 (1924), 211–223. DOI 10.1007/BF01187468 | MR 1544701
[5] Golab, S.: On semi-symmetric and quarter-symmetric linear connectionsTensor, N. S. : Tensor, N. S. 29 (1975), 249–254. MR 0383275
[6] Hayden, H. A.: Subspaces of a space with torsion. Proc. London Math. Soc. 34 (1932), 27–50. DOI 10.1112/plms/s2-34.1.27 | MR 1576150
[7] Hinterleitner, I., Mikeš, J.: Geodesic mappings and Einstein spaces. In: Geometric Methods in Physics, Trends in Mathematics, Birkhäuser, Basel, 2013, 331–335. MR 3364052 | Zbl 1268.53049
[8] Mikeš, J.: Differential Geometry of Special Mappings. Palacky Univ. Press, Olomouc, 2015. MR 3442960 | Zbl 1337.53001
[9] Mikeš, J.: Geodesic mappings of affine-connected and Riemannian spaces. J. Math. Sci. 78, 3 (1996), 311–333. DOI 10.1007/BF02365193 | MR 1384327
[10] Mikeš, J.: Holomorphically projective mappings and their generalizations. J. Math. Sci. 89, 3 (1998), 1334–1353. DOI 10.1007/BF02414875 | MR 1619720
[11] Mikeš, J., Vanžurová, A., Hinterleitner, I.: Geodesic Mappings and Some Generalizations. Palacky Univ. Press, Olomouc, 2009. MR 2682926 | Zbl 1222.53002
[12] Mikeš, J., Starko, G. A.: On hyperbolically Sasakian and equidistant hyperbolically Kählerian spaces. Ukr. Geom. Sb. 32 (1989), 92–98. MR 1049372 | Zbl 0711.53042
[13] Mikeš, J.: Equidistant Kähler spaces. Math. Notes 38 (1985), 855–858. DOI 10.1007/BF01158415 | MR 0819428 | Zbl 0594.53024
[14] Mikeš, J.: On Sasaki spaces and equidistant Kähler spaces. Sov. Math., Dokl. 34 (1987), 428–431. MR 0819428 | Zbl 0631.53018
[15] Mishra, R. S., Pandey, S. N.: On quarter-symmetric metric F-connection. Tensor, N. S. 34 (1980), 1–7. MR 0570556
[16] Prakashs, D. G., Bagewadi, C. S., Basavarajappa, N. S.: On pseudosymmetric Lorentzian $\alpha $-Sasakian manifolds. IJPAM 48, 1 (2008), 57–65. MR 2456434
[17] Rastogi, S. C.: On quarter-symmetric connection. C. R. Acad. Sci. Bulgar 31 (1978), 811–814. MR 0522544
[18] Rastogi, S. C.: On quarter-symmetric metric connection. Tensor 44 (1987), 133–141. MR 0944894
[19] Sinyukov, N. S.: Geodesic mappings of Riemannian spaces. Nauka, Moscow, 1979. Zbl 0637.53020
[20] Takahashi, T.: Sasakian $\phi $-symmetric spaces. Tohoku Math. J. 29 (1977), 91–113. DOI 10.2748/tmj/1178240699 | MR 0440472
[21] Tripathi, M. M., Dwivedi, M. K.: The structure of some classes of K-contact manifolds. Proc. Indian Acad. Sci. Math. Sci. 118 (2008), 371–379. DOI 10.1007/s12044-008-0029-1 | MR 2450241 | Zbl 1155.53020
[22] Yano, K.: On semi-symmetric metric connections. Rev. Roumaine Math. Pures Appl. 15 (1970), 1579–1586. MR 0275321
[23] Yano, K., Imai, T.: Quarter-symmetric metric connections and their curvature tensors. Tensor, N. S. 38 (1982), 13–18. MR 0832619 | Zbl 0504.53014
[24] Yildiz, A., Murathan, C.: On Lorentzian $\alpha $-Sasakian manifolds. Kyungpook Math. J. 45 (2005), 95–103. MR 2142281 | Zbl 1085.53023
[25] Yadav, S., Suthar, D. L.: Certain derivation on Lorentzian $\alpha $-Sasakian manifolds. Mathematics and Decision Science 12, 2 (2012), 1–6. MR 2814463
[26] Yildiz, A., Turan, M., Acet, B. F.: On three dimensional Lorentzian $\alpha $-Sasakian manifolds. Bulletin of Mathematical Analysis and Applications 1, 3 (2009), 90–98. MR 2578119 | Zbl 1312.53071
Search
Partner of
