In this paper, we study the geometry and topology of [Formula: see text]-Ricci solitons satisfying Ricci-semisymmetry condition, [Formula: see text] condition and finally Einstein-semisymmetry condition on nearly Kenmotsu manifolds.
In this work, we give some basic informations about Ricci solitons on nearly Kenmotsu manifolds and some structures on this manifolds satisfying semi-symmetric metric connection. Then we consider some important results and theorems of Ricci solitons on Ricci-recurrent and Φ −recurrent nearly Kenmotsu manifolds with semi-symmetric metric connection. Also final part of the present paper, we study Ricci solitons on quasi-projectively flat nearly Kenmotsu manifolds with semi-symmetric metric connection.
In 1966, B. O'Neill [The fundamental equations of a submersion, Michigan Math. J., Volume 13, Issue 4 (1966), 459-469.] obtained some fundamental equations and curvature relations between the total space, the base space and the fibres of a submersion. In the present paper, we define new curvature tensors along Riemannian submersions such as Weyl projective curvature tensor, concircular curvature tensor, conharmonic curvature tensor, conformal curvature tensor and M −projective curvature tensor, respectively. Finally, we obtain some results in case of the total space of Riemannian submersions has umbilical fibres for any curvature tensors mentioned by the above.
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