Jai Prakash Jaiswal, Arjun Singh Yadav

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The aim of the present paper is to study generalized M-projective - recurrent trans-Sasakian manifold and its various geometric properties. First, we find the sufficient condition for generalized M-projective -recurrent trans-Sasakian manifold to become Einstein. Then non-existence of generalized M-projective -recurrent trans-Sasakian manifold has been shown under certain condition. Finally, the sufficient condition for super generalized Ricci-recurrent was also established.


Trans-Sasakian manifold; M-projective curvature tensor; Generalized - recurrent; Einstein manifold; Super generalized Ricci-recurrent; Quasi-generalized Ricci- recurrent

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E. Cartan: Sur une classes remarquable d’espaces de Riemann, Bull. Soc. Math. France, 54 (1926), 214-264.

M. C. Chaki: On weakly symmetric manifolds, Analel stiintificae Ale Univeritatii Alenandru Ioan CuzzaIasi Romania, 33 (1987), 53-58.

S. K. Chaubey and R. H. Ojha On the m-projective curvature tensor of a Kenmotsu manifold, Diff. Geom. Dynam. Sys., 12 (2010), 52-60.

D. Debnath and A. Battacharyya: On generalized -recurrent trans-Sasakian manifolds, Acta Univ. Apule., 36 (2013), 253-266.

R. Deszcz: On pseudo-symmetric spaces, Acta Math. Hungar., 53 (1992), 481-482.

R. S. D. Dubey: Generalized recurrent spaces, Indian J. Pure Appl. Math., 10(12)(1979), 1508-1513.

U. C. De and A. K. Gazi: On generalized concircularly recurrent manifolds, Studia Sci. Math. Hungar., 46 (2009), 278-296.

U. C. De, A. A. Shaikh and S. Biswas: On -recurrent Sasakian manifolds, Novi Sad J. Math, 33 (2003), 13-48.

U. C. De and A. A. Shaikh: Complex manifolds and contact manifolds, Narosa Publ. (2009).

U. C. De and A. Sarkar: On 3-dimensional trans-Sakian manifolds, Ext. Math, 3 (2008), 265-277.

U. C. De and P. Pal: On generalized M-projectively recurrent manifolds, Ann. Univ. Paedagog. Crac. Stud. Math., 13 (2014), 77-101.

R. H. Ojha: A note on the m-projective curvature tensor, Indian J. Pure Appl. Math., 8 (12) (1975), 1531-1534.

R. H. Ojha: m-projectively flat Sasakian manifolds, Indian J. Pure Appl. Math., 17 (4) (1986), 1531-1534.

J. A. Oubina: New classes of almost contact metric structures, Publ. Math. Debrecen, 32 (1985), 21-38.

G. P. Pokhariyal and R. S. Mishra: Curvature tensors and their relativistic significance-ii, Yok. Math. J., 19 (1971), 97-103.

D. G. Prakasha: On Extended Generalized -Recurrent Sasakian Manifolds, J. Egypt. Math. Soc., 21 (2013), 25-31.

R. Prasad and V. Srivastava: Some results on trans-Sasakian manifolds, Math. Vesnik, 65 (2013), 346-352.

A. A. Shaikh and H. Ahmad: On generalized -recurrent Sasakian manifold, Appl. Math., 2 (2011), 1317-1322.

A. A. Shaikh and I. Roy: On quasi-generalized recurrent manifold, Math. Pannaonica, 21(2) (2010), 251-263.

J. P. Singh: On the M-projective curvature tensor of Sasakian manifold, Publ. Math. Debrec., 15(2) (2015), 76-79.

A. Selberg: Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series, Indian Math. Soc., 20 (1956), 47-87.

Z. I. Szabo: Structure theorems on Riemannian spaces satisfying R(X, Y ).R = 0. I. The local version, J. Diff. Geom., 17(4) (1982), 531-582.

L. Tamassy and T. Q. Binh: On weakly symmetric and weakly projective symmetric Riemannian manifold, Colloquia Math. Soc., 50 (1989), 663-667.

A. A. Walker: On Ruses spaces of recurrent curvature, Proc. London. Math.Soc., 52 (1950), 36-64.

T. Takahashi: Sasakian -symmetric space, Tohoku Math. J., 29 (1977), 91-113.


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