In the present paper, we introduce slant Riemannian maps from an almost contact manifold to Riemannian manifolds. We obtain the existence condition of slant Riemannian maps from an almost contact manifold to Riemannian manifolds. Moreover, we find the necessary and sufficient condition for slant Riemannian map to be totally geodesic and investigate the harmonicity of slant Riemannian maps from Sasakian manifold to Riemannian manifolds. Finally, we obtain a decomposition theorem for the total manifolds and also provide some examples of such maps.

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Abstract:The object of the present paper is to study a semi-symmetric non-metric connection in an indefinite para Sasakian manifold. In this paper, we obtain the relation between the semi-symmetric non-metric connection and Levi-Civita connection in an indefinite para Sasakian manifold. Also, the Nijenhuis tensor, curvature tensor and projective curvature tensor of semi-symmetric non-metric connection in an indefinite para Sasakian manifold have been studied.

The objective of present research article is to investigate the geometric properties of $\eta$-Ricci solitons on Lorentzian para-Kenmotsu manifolds. In this manner, we consider $\eta$-Ricci solitons on Lorentzian para-Kenmotsu manifolds satisfying $R\cdot S=0$. Further, we obtain results for $\eta$-Ricci solitons on Lorentzian para-Kenmotsu manifolds with quasi-conformally flat property. Moreover, we get results for $\eta$-Ricci solitons in Lorentzian para-Kenmotsu manifolds admitting Codazzi type of Ricci tensor and cyclic parallel Ricci tensor, $\eta$-quasi-conformally semi-symmetric, $\eta$-Ricci symmetric and quasi-conformally Ricci semi-symmetric. At last, we construct an example of a such manifold which justify the existence of proper $\eta$-Ricci solitons.

In this paper, we consider $\left(LCS\right)_{n}$ manifold admitting almost $\eta-$Ricci solitons by means of curvature tensors. Ricci pseudosymmetry concepts of $\left(LCS\right)_{n}$ manifold admitting $\eta-$Ricci soliton have introduced according to the choice of some special curvature tensors such as pseudo-projective, $W_{1}$, $W_{1}^{\ast}$ and $W_{2}.$ Then, again according to the choice of the curvature tensor, necessary conditions are searched for $\left(LCS\right)_{n}$ manifold admitting $\eta-$Ricci soliton to be Ricci semisymmetric. Then some characterizations are obtained and some classifications have made.