×

Results on para-Sasakian manifold admitting a quarter symmetric metric connection. (English) Zbl 1454.53029

Summary: In this paper we have studied pseudosymmetric, Ricci-pseudosymmetric and projectively pseudosymmetric para-Sasakian manifold admitting a quarter-symmetric metric connection and constructed examples of 3-dimensional and 5-dimensional para-Sasakian manifold admitting a quarter-symmetric metric connection to verify our results.

MSC:

53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Abul Kalam Mondal and U.C. De, Quarter-symmetric nonmetric Connection on P-Sasakian manifolds, ISRN Geometry, (2012), 1-14. · Zbl 1256.53013
[2] G. Soos, Uber die geodatischen Abbildungen von Riemannaschen Raumen auf projektivsymmetrische Riemannsche Raume, Acta. Math. Acad. Sci. Hungar., 9, (1958), 359-361 · Zbl 0085.36903
[3] A. Barman, Concircular curvature tensor on a P-Sasakian manifold admitting a quartersymmetric metric connection, Kragujevac J. Math. 42 (2018), 2, 275-285. · Zbl 1488.53086
[4] D. V. Alekseevsky et al. , Cones over pseudo-Riemannian manifolds and their holonomy, J. Reine Angew. Math. 635 (2009), 23-69. · Zbl 1181.53057
[5] E. Cartan, Surune classe remarquable d’espaces de Riema, Soc. Math., France, 54 (1926), 214-264. · JFM 53.0390.01
[6] Cihan Ozgur, On A class of para-Sakakian manifolds, Turk J Math. , 29 (2005), 249-257. · Zbl 1092.53015
[7] V. Cortes et al., Special geometry of Euclidean supersymmetry. I. Vector multiplets, J. High Energy Phys. , 03, (2004), 1-64.
[8] V. Cortes, M.-A. Lawn and L. Schafer, Affine hyperspheres associated to special para-Kahler manifolds, Int. J. Geom. Methods Mod. Phys. 3 (2006), 5-6, 995-1009. · Zbl 1122.53006
[9] R. Deszcz, On pseudosymmetric spaces, Acta Math., Hungarica, 53 (1992), 185-190. · Zbl 0808.53012
[10] R. Deszcz and S. Yaprak, Curvature properties of certain pseudosymmetric manifolds, Publ. Math. Debrecen 45 (1994), 3-4, 333-345. · Zbl 0827.53031
[11] R. Deszcz et al., On some curvature conditions of pseudosymmetry type, Period. Math. Hungar. 70 (2015), 2, 153-170. · Zbl 1374.53030
[12] S. Golab, On semi-symmetric and quarter-symmetric linear connections, Tensor (N.S.) 29 (1975), 3, 249-254. · Zbl 0308.53010
[13] S. Haesen and L. Verstraelen, Properties of a scalar curvature invariant depending on two planes, Manuscripta Math. 122 (2007), 1, 59-72. · Zbl 1109.53020
[14] S. Kaneyuki and F. L. Williams, Almost paracontact and parahodge structures on manifolds, Nagoya Math. J. 99 (1985), 173-187. · Zbl 0576.53024
[15] Lata Bisht and Sandhana Shanker, Curvature tensor on para-Sasakian manifold admitting quarter symmetric metric connection, IOSR Journal of Mathematics, 11(5), (2015), 22-28.
[16] K. Mandal and U. C. De, Quarter-symmetric metric connection in a P-Sasakian manifold, An. Univ. Vest Timis. Ser. Mat.-Inform. 53 (2015), 1, 137-150. · Zbl 1374.53081
[17] K.T. Pradeep Kumar, Venkatesha and C. S. Bagewadi, On_-recurrent para-Sasakian manifold admitting quarter-symmetric metric connection, ISRN Geometry , (2012), 1-10. · Zbl 1239.53037
[18] I. Sato, On a structure similar to the almost contact structure, Tensor (N.S.) 30 (1976), 3, 219-224. · Zbl 0344.53025
[19] Z. I. Szabo, Structure theorems on Riemannian spaces satisfying R(X, Y ) ・R = 0. I. The local version, J. Differential Geometry 17 (1982), 4, 531-582 · Zbl 0508.53025
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.