| Title:
|
Some Properties of Lorentzian $\alpha $-Sasakian Manifolds with Respect to Quarter-symmetric Metric Connection (English) |
| Author:
|
DEY, Santu |
| Author:
|
BHATTACHARYYA, Arindam |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
54 |
| Issue:
|
2 |
| Year:
|
2015 |
| Pages:
|
21-40 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The aim of this paper is to study generalized recurrent, generalized Ricci-recurrent, weakly symmetric and weakly Ricci-symmetric, semi-generalized recurrent, semi-generalized Ricci-recurrent Lorentzian $\alpha $-Sasakian manifold with respect to quarter-symmetric metric connection. Finally, we give an example of 3-dimensional Lorentzian $\alpha $-Sasakian manifold with respect to quarter-symmetric metric connection. (English) |
| Keyword:
|
Quarter-symmetric metric connection |
| Keyword:
|
Lorentzian $\alpha $-Sasakian manifold |
| Keyword:
|
generalized recurrent manifold |
| Keyword:
|
generalized Ricci-recurrent manifold |
| Keyword:
|
weakly symmetric manifold |
| Keyword:
|
weakly Ricci-symmetric manifold |
| Keyword:
|
semi-generalized recurrent manifold |
| Keyword:
|
Einstein manifold |
| MSC:
|
53C15 |
| MSC:
|
53C25 |
| idZBL:
|
Zbl 1346.53032 |
| idMR:
|
MR3469689 |
| . |
| Date available:
|
2015-12-21T17:04:01Z |
| Last updated:
|
2018-01-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144761 |
| . |
| Reference:
|
[1] Chaki, M. C.: On pseudo symmetric manifolds. An. Stiint. Univ. Al. I. Cuza Iasi Sect. I a Mat. 33, 1 (1987), 53–58. Zbl 0634.53012, MR 0925690 |
| Reference:
|
[2] Chaki, M. C.: On pseudo Ricci symmetric manifolds. Bulgar. J. Phys. 15, 6 (1988), 526–531. Zbl 0689.53011, MR 1028590 |
| Reference:
|
[3] Chaki, M. C.: Some theorems on recurrent and Ricci-recurrent spaces. Rend. Sem. Math. Delta Univ. Padova 26 (1956), 168–176. Zbl 0075.17501, MR 0084165 |
| Reference:
|
[4] Deszcz, R., Kowalczyk, D.: On some class of pseudosymmetric warped products. Colloq. Math. 97, 1 (2003), 7–22. Zbl 1053.53017, MR 2010538, 10.4064/cm97-1-2 |
| Reference:
|
[5] Friedmann, A., Schouten, J. A.: Uber die Geometrie der halbsymmetrischen Uber-tragung. Math. Zeitschr. 21 (1924), 211–223. MR 1544701, 10.1007/BF01187468 |
| Reference:
|
[6] Golab, S.: On semi-symmetric and quarter-symmetric linear connections. Tensor, N.S. 29 (1975), 249–254. Zbl 0308.53010, MR 0383275 |
| Reference:
|
[7] Hayden, H. A.: Subspaces of a space with torsion. Proc. London Math. Soc. 34 (1932), 27–50. MR 1576150 |
| Reference:
|
[8] Mishra, R. S., Pandey, S. N.: On quarter-symmetric metric F-connection. Tensor, N.S. 34 (1980), 1–7. MR 0570556 |
| Reference:
|
[9] Mikeš, J.: Geodesic Ricci mappings of two-symmetric Riemann spaces. Math. Notes 28 (1981), 622–624. Zbl 0454.53013, 10.1007/BF01157926 |
| Reference:
|
[10] Mikeš, J.: Geodesic mappings of affine-connected and Riemannian spaces. J. Math. Sci. 78, 3 (1996), 311–333. MR 1384327, 10.1007/BF02365193 |
| Reference:
|
[11] Mikeš, J., Vanžurová, A., Hinterleitner, I.: Geodesic mappings and some generalizations. Palacký University, Olomouc, 2009. Zbl 1222.53002, MR 2682926 |
| Reference:
|
[12] Mikeš et al., J.: Differential geometry of special mappings. Palacky University, Olomouc, 2015. Zbl 1337.53001, MR 3442960 |
| Reference:
|
[13] Mikeš, J.: Geodesic mappings of special Riemannian spaces. Topics in differential geometry, Vol. II, Colloq. Math. Soc. János Bolyai, Debrecen 46 (1984), North-Holland, Amsterdam. MR 0933875 |
| Reference:
|
[14] Mikeš, J., Rachůnek, L.: Torse-forming vector fields in T-semisymmetric Riemannian spaces. In: Steps in Differential Geometry. Proc. Colloq. Diff. Geometry, Univ. Debrecen, Inst. Math. and Inf., Debrecen, 2001, 219–229. Zbl 0994.53009, MR 1859300 |
| Reference:
|
[15] Mikeš, J., Rachůnek, L.: T-semisymmetric spaces and concircular vector fields. Rend. Circ. Mat. Palermo, II. Suppl. 69 (2002), 187–193. Zbl 1023.53014, MR 1972434 |
| Reference:
|
[16] Mukhopadhyay, S., Roy, A. K., Barua, B.: Some properties of a quartersymmetric metric connection on a Riemannian manifold. Soochow J. Math. 17 (1991), 205–211. MR 1143507 |
| Reference:
|
[17] Patterson, K. M.: Some theorem on Ricci-recurrent spaces. London Math. Soc. 27 (1952), 287–295. MR 0048891, 10.1112/jlms/s1-27.3.287 |
| Reference:
|
[18] Prakash, N.: A note on Ricci-recurrent and recurrent spaces. Bulletin of the Calcutta Mathematical Society 54 (1962), 1–7. MR 0148007 |
| Reference:
|
[19] Prasad, B.: On semi-generalized recurrent manifold. Mathematica Balkanica, New series 14 (2000), 77–82. Zbl 1229.53020, MR 1818271 |
| Reference:
|
[20] Prakashs, D. G., Bagewadi, C. S., Basavarajappa, N. S.: On pseudosymmetric Lorentzian $\alpha $-Sasakian manifolds. IJPAM 48, 1 (2008), 57–65. MR 2456434 |
| Reference:
|
[21] Khan, Q.: On generalized recurrent Sasakian manifolds. Kyungpook Math. J. 44 (2004), 167–172. Zbl 1086.53064, MR 2064777 |
| Reference:
|
[22] Rastogi, S. C.: On quarter-symmetric connection. C. R. Acad. Sci. Bulgar 31 (1978), 811–814. MR 0522544 |
| Reference:
|
[23] Rastogi, S. C.: On quarter-symmetric metric connection. Tensor 44 (1987), 133–141. MR 0944894 |
| Reference:
|
[24] Ruse, H. S.: A classification of $K^{*}$-spaces. London Math. Soc. 53 (1951), 212–229. Zbl 0045.43001, MR 0043536, 10.1112/plms/s2-53.3.212 |
| Reference:
|
[25] Rachůnek, L., Mikeš, J.: On tensor fields semiconjugated with torse-forming vector fields. Acta Univ. Palacki. Olomuc., Fac. Rer. Nat., Math. 44 (2005), 151–160. Zbl 1092.53016, MR 2218574 |
| Reference:
|
[26] Sular, S.: Some properties of a Kenmotsu manifold with a semi symmetric metric connection. Int. Electronic J. Geom. 3 (2010), 24–34. Zbl 1190.53042, MR 2639328 |
| Reference:
|
[27] Tamassy, L., Binh, T. Q.: On weakly symmetric and weakly projective symmetric Riemannian manifolds. Coll. Math. Soc. J. Bolyai 56 (1992), 663–670. Zbl 0791.53021, MR 1211691 |
| Reference:
|
[28] Tamassy, L., Binh, T. Q.: On weak symmetries of Einstein and Sasakian manifolds. Tensor, N.S. 53 (1993), 140–148. Zbl 0849.53038, MR 1455411 |
| Reference:
|
[29] Tripathi, M. M.: On a semi-symmetric metric connection in a Kenmotsu manifold. J. Pure Math. 16 (1999), 67–71. Zbl 1053.53508, MR 1768254 |
| Reference:
|
[30] Tripathi, M. M.: A new connection in a Riemannian manifold. Int. Electronic J. Geom. 1 (2008), 15–24. Zbl 1135.53007, MR 2390386 |
| Reference:
|
[31] Tripathi, M. M., Nakkar, N.: On a semi-symmetric non-metric connection in a Kenmotsu manifold. Bull. Cal. Math. Soc. 16, 4 (2001), 323–330. MR 1909351 |
| Reference:
|
[32] Yano, K.: On semi-symmetric metric connections. Rev. Roumaine Math. Pures Appl. 15 (1970), 1579–1586. MR 0275321 |
| Reference:
|
[33] 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:
|
[34] Yadav, S., Suthar, D. L.: Certain derivation on Lorentzian $\alpha $-Sasakian manifolds. Mathematics and Decision Science 12, 2 (2012), 1–6. MR 2814463 |
| Reference:
|
[35] Yamaguchi, S., Matsumoto, M.: On Ricci-recurrent spaces. Tensor, N.S. 19 (1968), 64–68. Zbl 0168.19503, MR 0221430 |
| Reference:
|
[36] Yildiz, A., Murathan, C.: On Lorentzian $\alpha $-Sasakian manifolds. Kyungpook Math. J. 45 (2005), 95–103. Zbl 1085.53023, MR 2142281 |
| Reference:
|
[37] Yildiz, A., Turan, M., Acet, B. F.: On three dimensional Lorentzian $\alpha $-Sasakian manifolds. Bull. Math. Anal. Appl. 1, 3 (2009), 90–98. Zbl 1312.53071, MR 2578119 |
| . |
