Geodesic
Some Classes of Lorentzian $\alpha $-Sasakian Manifolds Admitting a Quarter-symmetric Metric Connection
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 55 (2016) no. 2, pp. 41-55 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 53C15, 53C25
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 
@article{AUPO_2016_55_2_a4,
     author = {DEY, Santu and Pal, Buddhadev and BHATTACHARYYA, Arindam},
     title = {Some {Classes} of {Lorentzian} $\alpha ${-Sasakian} {Manifolds} {Admitting} {a~Quarter-symmetric} {Metric} {Connection}},
     journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
     pages = {41--55},
     year = {2016},
     volume = {55},
     number = {2},
     zbl = {1365.53045},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AUPO_2016_55_2_a4/}
}
TY  - JOUR
AU  - DEY, Santu
AU  - Pal, Buddhadev
AU  - BHATTACHARYYA, Arindam
TI  - Some Classes of Lorentzian $\alpha $-Sasakian Manifolds Admitting a Quarter-symmetric Metric Connection
JO  - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY  - 2016
SP  - 41
EP  - 55
VL  - 55
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/AUPO_2016_55_2_a4/
LA  - en
ID  - AUPO_2016_55_2_a4
ER  - 
%0 Journal Article
%A DEY, Santu
%A Pal, Buddhadev
%A BHATTACHARYYA, Arindam
%T Some Classes of Lorentzian $\alpha $-Sasakian Manifolds Admitting a Quarter-symmetric Metric Connection
%J Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
%D 2016
%P 41-55
%V 55
%N 2
%U http://geodesic.mathdoc.fr/item/AUPO_2016_55_2_a4/
%G en
%F AUPO_2016_55_2_a4
DEY, Santu; Pal, Buddhadev; BHATTACHARYYA, Arindam. Some Classes of Lorentzian $\alpha $-Sasakian Manifolds Admitting a Quarter-symmetric Metric Connection. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 55 (2016) no. 2, pp. 41-55. http://geodesic.mathdoc.fr/item/AUPO_2016_55_2_a4/

[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 | Zbl

[2] Boeckx, E., Buecken, P., Vanhecke, L.: $\phi $-symmetric contact metric spaces. Glasgow Math. J. 41 (1999), 409–416. | DOI | MR

[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 | MR

[5] Golab, S.: On semi-symmetric and quarter-symmetric linear connectionsTensor, N. S. : Tensor, N. S. 29 (1975), 249–254. | MR

[6] Hayden, H. A.: Subspaces of a space with torsion. Proc. London Math. Soc. 34 (1932), 27–50. | DOI | MR

[7] Hinterleitner, I., Mikeš, J.: Geodesic mappings and Einstein spaces. In: Geometric Methods in Physics, Trends in Mathematics, Birkhäuser, Basel, 2013, 331–335. | MR | Zbl

[8] Mikeš, J.: Differential Geometry of Special Mappings. Palacky Univ. Press, Olomouc, 2015. | MR | Zbl

[9] Mikeš, J.: Geodesic mappings of affine-connected and Riemannian spaces. J. Math. Sci. 78, 3 (1996), 311–333. | DOI | MR

[10] Mikeš, J.: Holomorphically projective mappings and their generalizations. J. Math. Sci. 89, 3 (1998), 1334–1353. | DOI | MR

[11] Mikeš, J., Vanžurová, A., Hinterleitner, I.: Geodesic Mappings and Some Generalizations. Palacky Univ. Press, Olomouc, 2009. | MR | Zbl

[12] Mikeš, J., Starko, G. A.: On hyperbolically Sasakian and equidistant hyperbolically Kählerian spaces. Ukr. Geom. Sb. 32 (1989), 92–98. | MR | Zbl

[13] Mikeš, J.: Equidistant Kähler spaces. Math. Notes 38 (1985), 855–858. | DOI | MR | Zbl

[14] Mikeš, J.: On Sasaki spaces and equidistant Kähler spaces. Sov. Math., Dokl. 34 (1987), 428–431. | MR | Zbl

[15] Mishra, R. S., Pandey, S. N.: On quarter-symmetric metric F-connection. Tensor, N. S. 34 (1980), 1–7. | MR

[16] Prakashs, D. G., Bagewadi, C. S., Basavarajappa, N. S.: On pseudosymmetric Lorentzian $\alpha $-Sasakian manifolds. IJPAM 48, 1 (2008), 57–65. | MR

[17] Rastogi, S. C.: On quarter-symmetric connection. C. R. Acad. Sci. Bulgar 31 (1978), 811–814. | MR

[18] Rastogi, S. C.: On quarter-symmetric metric connection. Tensor 44 (1987), 133–141. | MR

[19] Sinyukov, N. S.: Geodesic mappings of Riemannian spaces. Nauka, Moscow, 1979. | Zbl

[20] Takahashi, T.: Sasakian $\phi $-symmetric spaces. Tohoku Math. J. 29 (1977), 91–113. | DOI | MR

[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 | MR | Zbl

[22] Yano, K.: On semi-symmetric metric connections. Rev. Roumaine Math. Pures Appl. 15 (1970), 1579–1586. | MR

[23] Yano, K., Imai, T.: Quarter-symmetric metric connections and their curvature tensors. Tensor, N. S. 38 (1982), 13–18. | MR | Zbl

[24] Yildiz, A., Murathan, C.: On Lorentzian $\alpha $-Sasakian manifolds. Kyungpook Math. J. 45 (2005), 95–103. | MR | Zbl

[25] Yadav, S., Suthar, D. L.: Certain derivation on Lorentzian $\alpha $-Sasakian manifolds. Mathematics and Decision Science 12, 2 (2012), 1–6. | MR

[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 | Zbl