Generalized Sasakian space forms have become today a rather specialized subject, but many contemporary works are concerned with the study of their properties and of their related curvature tensors. The goal of this paper is to study the E-Bochner curvature tensor on generalized Sasakian space forms, and to characterize the situations when it is, respectively: E-Bochner symmetric (); E-Bochner semisymmetric (); E-Bochner recurrent; E-Bochner pseudosymmetric; such that ; such that .
Les espaces formes sasakiens généralisés sont devenus aujourd'hui un sujet assez spécialisé, mais de nombreux travaux contemporains s'attachent à l'étude de leurs propriétés et des tenseurs de courbure associés. Le but de cette note est d'étudier le tenseur de courbure de type E-Bochner sur les espaces formes sasakiens généralisés, et de caractériser les conditions pour qu'il soit respectivement : E-Bochner symétrique () ; E-Bochner semi-symétrique () ; E-Bochner récurrent ; E-Bochner pseudo-symétrique ; tel que ; tel que .
Accepted:
Published online:
D.G. Prakasha 1; Vasant Chavan 1
@article{CRMATH_2016__354_8_835_0, author = {D.G. Prakasha and Vasant Chavan}, title = {E-Bochner curvature tensor on generalized {Sasakian} space forms}, journal = {Comptes Rendus. Math\'ematique}, pages = {835--841}, publisher = {Elsevier}, volume = {354}, number = {8}, year = {2016}, doi = {10.1016/j.crma.2015.10.027}, language = {en}, }
D.G. Prakasha; Vasant Chavan. E-Bochner curvature tensor on generalized Sasakian space forms. Comptes Rendus. Mathématique, Volume 354 (2016) no. 8, pp. 835-841. doi : 10.1016/j.crma.2015.10.027. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.10.027/
[1] Generalized Sasakian space forms, Isr. J. Math., Volume 14 (2004), pp. 157-183
[2] Structures on generalized Sasakian space forms, Differ. Geom. Appl., Volume 26 (2008), pp. 656-666
[3] Submanifolds generalized Sasakian space forms, Taiwan. J. Math., Volume 13 (2009), pp. 923-941
[4] Generalized Sasakian space forms and conformal change of metric, Results Math., Volume 59 (2011), pp. 485-493
[5] Contact Manifolds in Riemannian Geometry, Lecture Notes in Mathematics, vol. 509, Springer-Verlag, 1976
[6] On the geometric meaning of the Bochner tensor, Geom. Dedic., Volume 4 (1975), pp. 33-38
[7] Curvature and Betti numbers, Ann. of Math., Volume 50 (1949), pp. 77-93
[8] On contact manifolds, Ann. of Math. (2), Volume 68 (1958), pp. 721-734
[9] On the projective curvature tensor of generalized Sasakian space forms, Quaest. Math., Volume 33 (2010), pp. 245-252
[10] E-Bochner curvature tensor on -contact metric manifolds, Int. Electron. J. Geom., Volume 7 (2014) no. 1, pp. 143-153
[11] E-Bochner curvature tensor on -contact metric manifolds, Hacet. J. Math. Stat., Volume 43 (2014) no. 3, pp. 365-374
[12] On pseudosymmetric spaces, Bull. Soc. Math. Belg., Sér. A, Volume 44 (1992) no. 1, pp. 1-34
[13] On K-contact Riemannian manifolds with vanishing E-contact Bochner curvature tensor, Colloq. Math., Volume 62 (1991), pp. 293-297
[14] On the -curvature tensor of generalized Sasakian space forms, Math. Pannon., Volume 23 (2012) no. 1, pp. 113-124
[15] Conformally flat generalized Sasakian space forms and locally symmetric generalized Sasakian space forms, Note Mat., Volume 26 (2006), pp. 55-67
[16] On C-Bochner curvature tensor of a contact metric manifold, Bull. Korean Math. Soc., Volume 42 (2005), pp. 713-724
[17] On the C-Bochner curvature tensor, TRU Math., Volume 5 (1969), pp. 21-30
[18] On hypersurfaces satisfying a certain condition on the curvature tensor, Tohoku Math. J., Volume 20 (1968), p. 46
[19] Condition for a compact Kahlerian space to be locally symmetric, Nat. Sci. Rep. Ochanomizu Univ., Volume 28 (1971), p. 21
[20] Contact manifolds with C-Bochner curvature tensor, Bull. Calcutta Math. Soc., Volume 96 (2004) no. 1, pp. 45-50
[21] On generalized Sasakian space forms with Weyl-conformal curvature tensor, Lobachevskii J. Math., Volume 33 (2012) no. 3, pp. 223-228
[22] On quasi-conformally flat and quasi-conformally semisymmetric generalized Sasakian space forms, CUBO, Volume 15 (2013) no. 3, pp. 59-70
[23] Structure theorems on Riemannian spaces satisfying . The local version, J. Differ. Geom., Volume 17 (1982), pp. 531-582
[24] Locally symmetric K-contact Riemannian manifold, Proc. Jpn. Acad., Volume 43 (1967), p. 581
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