| Title:
|
Some Classes of Lorentzian $\alpha $-Sasakian Manifolds Admitting a Quarter-symmetric Metric Connection (English) |
| Author:
|
DEY, Santu |
| Author:
|
Pal, Buddhadev |
| Author:
|
BHATTACHARYYA, Arindam |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
55 |
| Issue:
|
2 |
| Year:
|
2016 |
| Pages:
|
41-55 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
Quarter-symmetric metric connection |
| Keyword:
|
Lorentzian $\alpha $-Sasakian manifold |
| Keyword:
|
locally $\phi $-symmetric manifold |
| Keyword:
|
locally projective $\phi $-symmetric manifold |
| Keyword:
|
$\xi $-projectively flat Lorentzian $\alpha $-Sasakian manifold |
| MSC:
|
53C15 |
| MSC:
|
53C25 |
| idZBL:
|
Zbl 1365.53045 |
| . |
| Date available:
|
2017-03-16T12:39:57Z |
| Last updated:
|
2018-01-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146060 |
| . |
| Reference:
|
[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. Zbl 1159.53323, MR 2483702 |
| Reference:
|
[2] Boeckx, E., Buecken, P., Vanhecke, L.: $\phi $-symmetric contact metric spaces.. Glasgow Math. J. 41 (1999), 409–416. MR 1720426, 10.1017/S0017089599000579 |
| Reference:
|
[3] Formella, S., Mikeš, J.: Geodesic mappings of Einstein spaces.. Ann. Sci. Stetinenses 9 (1994), 31–40. |
| Reference:
|
[4] Friedmann, A., Schouten, J. A.: Uber die Geometrie der halbsymmetrischen Uber-tragung.. Math. Zeitschr 21 (1924), 211–223. MR 1544701, 10.1007/BF01187468 |
| Reference:
|
[5] Golab, S.: On semi-symmetric and quarter-symmetric linear connectionsTensor, N. S..: Tensor, N. S. 29 (1975), 249–254. MR 0383275 |
| Reference:
|
[6] Hayden, H. A.: Subspaces of a space with torsion.. Proc. London Math. Soc. 34 (1932), 27–50. MR 1576150, 10.1112/plms/s2-34.1.27 |
| Reference:
|
[7] Hinterleitner, I., Mikeš, J.: Geodesic mappings and Einstein spaces.. In: Geometric Methods in Physics, Trends in Mathematics, Birkhäuser, Basel, 2013, 331–335. Zbl 1268.53049, MR 3364052 |
| Reference:
|
[8] Mikeš, J.: Differential Geometry of Special Mappings.. Palacky Univ. Press, Olomouc, 2015. Zbl 1337.53001, MR 3442960 |
| Reference:
|
[9] Mikeš, J.: Geodesic mappings of affine-connected and Riemannian spaces.. J. Math. Sci. 78, 3 (1996), 311–333. MR 1384327, 10.1007/BF02365193 |
| Reference:
|
[10] Mikeš, J.: Holomorphically projective mappings and their generalizations.. J. Math. Sci. 89, 3 (1998), 1334–1353. MR 1619720, 10.1007/BF02414875 |
| Reference:
|
[11] Mikeš, J., Vanžurová, A., Hinterleitner, I.: Geodesic Mappings and Some Generalizations.. Palacky Univ. Press, Olomouc, 2009. Zbl 1222.53002, MR 2682926 |
| Reference:
|
[12] Mikeš, J., Starko, G. A.: On hyperbolically Sasakian and equidistant hyperbolically Kählerian spaces.. Ukr. Geom. Sb. 32 (1989), 92–98. Zbl 0711.53042, MR 1049372 |
| Reference:
|
[13] Mikeš, J.: Equidistant Kähler spaces.. Math. Notes 38 (1985), 855–858. Zbl 0594.53024, MR 0819428, 10.1007/BF01158415 |
| Reference:
|
[14] Mikeš, J.: On Sasaki spaces and equidistant Kähler spaces.. Sov. Math., Dokl. 34 (1987), 428–431. Zbl 0631.53018, MR 0819428 |
| Reference:
|
[15] Mishra, R. S., Pandey, S. N.: On quarter-symmetric metric F-connection.. Tensor, N. S. 34 (1980), 1–7. MR 0570556 |
| Reference:
|
[16] Prakashs, D. G., Bagewadi, C. S., Basavarajappa, N. S.: On pseudosymmetric Lorentzian $\alpha $-Sasakian manifolds.. IJPAM 48, 1 (2008), 57–65. MR 2456434 |
| Reference:
|
[17] Rastogi, S. C.: On quarter-symmetric connection.. C. R. Acad. Sci. Bulgar 31 (1978), 811–814. MR 0522544 |
| Reference:
|
[18] Rastogi, S. C.: On quarter-symmetric metric connection.. Tensor 44 (1987), 133–141. MR 0944894 |
| Reference:
|
[19] Sinyukov, N. S.: Geodesic mappings of Riemannian spaces.. Nauka, Moscow, 1979. Zbl 0637.53020 |
| Reference:
|
[20] Takahashi, T.: Sasakian $\phi $-symmetric spaces.. Tohoku Math. J. 29 (1977), 91–113. MR 0440472, 10.2748/tmj/1178240699 |
| Reference:
|
[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. Zbl 1155.53020, MR 2450241, 10.1007/s12044-008-0029-1 |
| Reference:
|
[22] Yano, K.: On semi-symmetric metric connections.. Rev. Roumaine Math. Pures Appl. 15 (1970), 1579–1586. MR 0275321 |
| Reference:
|
[23] Yano, K., Imai, T.: Quarter-symmetric metric connections and their curvature tensors.. Tensor, N. S. 38 (1982), 13–18. Zbl 0504.53014, MR 0832619 |
| Reference:
|
[24] Yildiz, A., Murathan, C.: On Lorentzian $\alpha $-Sasakian manifolds.. Kyungpook Math. J. 45 (2005), 95–103. Zbl 1085.53023, MR 2142281 |
| Reference:
|
[25] Yadav, S., Suthar, D. L.: Certain derivation on Lorentzian $\alpha $-Sasakian manifolds.. Mathematics and Decision Science 12, 2 (2012), 1–6. MR 2814463 |
| Reference:
|
[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. Zbl 1312.53071, MR 2578119 |
| . |
