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Murgescu (1970) explored generalized weyl spaces, while Negi (2017) Investigated Kaehlerian conharmonic bi-recurrent spaces. Subsequently, Negi (2018) delved into hyper asymptotic curves on Kaehlerian hypersurfaces. In this current work, the author computes Kaehlerian projective recurrent manifolds of umbilical hypersurfaces with a comprehensive weyl conharmonic recurrent curvature tensor and the projective recurrent curvature tensor.

[...]we obtain some results in case of the total space of Riemannian submersions has umbilical fibres for any curvature tensors mentioned by the above. 2010 Mathematics Subject Classification: 53C15, 53B20 Keywords: Riemannian submersion, Weyl projective curvature tensor, M-projective curvature tensor, concircular curvature tensor, conformal curvature tensor, conharmonic curvature tensor 1. (Af, g) and iG.gf Riemannian manifolds, a Riemannian submersion and RM, RG and R be Riemannian curvature tensors cf M,G and (7t 1 fibre respectively. In this case, for any U,V G %' (Af) and X,Y G the Ricci tensor SM holds the following equations [ ]: Proposition 2. [ ] Let's take the scalar curvatures cf lM,gflG,gf Riemannian manifolds and x E G,U-1 (pd) fibre with rM ,rG and r, respectively. Let, lM,gļ and lG,gf Riemannian manifolds, a Riemannian submersion and RM, RG and R be Riemannian cun'ature tensors, SM, SG and S be Ricci tensors cfM. Let 71: fMl8^ -> (G,#') be a Riemannian submersion, where (M^g) and (G,8Y Riemannian manifolds, if the Riemannian submersion has total umbilical fibres that is N = 0 and then the Weyl projective curvature tensor is given by and forany U,V,W,F G %\"(M) andX,Y,Z,H G 3. Let, (M,g) and (G,gf Riemannian manifolds, a Riemannian submersion and RM, RG and Ŕ be Riemannian curvature tensors, r64, rG and r be scalar curvature tensors cf M. G and the fibre respectively.

We study conformal η -Einstein solitons on the framework of trans-Sasakian manifold in dimension three. Existence of conformal η -Einstein solitons on trans-Sasakian manifold is discussed. Then we find some results on trans-Sasakian manifold which are conformal η -Einstein solitons where the Ricci tensor is cyclic parallel and Codazzi type. We also consider some curvature conditions with addition to conformal η -Einstein solitons on trans-Sasakian manifold. We also use torse-forming vector fields in addition to conformal η -Einstein solitons on trans-Sasakian manifold. Finally, an example of conformal η -Einstein solitons on trans-Sasakian manifold is constructed.

In this paper, we explore the characteristics of Lorentzian β - Kenmotsu manifolds admitting M - projective curvature tensor. We demonstrate that M - projectively flat and irrotational M - projective curvature tensor of Lorentzian β - Kenmotsu manifolds are locally isometric to hyperbolic space Hn(c), where c = -β2. Further, we deal with the M - projectively flat Lorentzian β - Kenmotsu manifold satisfies the condition R(X, Y ) . S = 0. The Lorentzian β - Kenmostu manifold with conservative M - projective curvature tensor is the subject of our next analysis. Finally, we obtain certain geometrical facts if the Lorentzian β - Kenmotsu manifold satisfying the relation M(X, Y ) . R = 0.

This paper concerns certain properties of projective curvature tensor, conharmonic curvature tensor, quasi-conharmonic curvature tensor, and Ricci semi-symmetric conditions with respect to the general connection in an LP-Sasakian manifold. We also provide the applications of LP-Sasakian manifolds admitting general connections in the context of the general theory of relativity.

The present paper deals with the investigations of a Kenmotsu manifold satisfying certain curvature conditions endowed with ★-η-Ricci solitons. First we find some necessary conditions for such a manifold to be φ-Einstein. Then, we study the notion of ★-η-Ricci soliton on this manifold and prove some significant results related to this notion. Finally, we construct a nontrivial example of three-dimensional Kenmotsu manifolds to verify some of our results.

The objective of the present findings is to analyze Kenmotsu manifolds by using (α, β) type generalized symmetric metric connection. The characterization of Kenmotsu manifold by using certain curvature properties corresponding to the generalized symmetric metric connection is investigated. In the end, an example of Kenmotsu manifold with the generalized symmetric metric connection admitting Q tensor and Weyl conformal curvature tensor is constructed by using partial differential equations.

The objective of the present paper is to introduce a special type of semi-symmetric metric connection ∇∗ on weakly symmetric Kähler manifolds to reduce the manifold, which is Einstein and Ricci flat. Also, we use a non-flat Riemannian manifold called a weakly concircular symmetric manifold and study its geometric properties on a weakly symmetric Kähler manifold endowed with a special type of semi-symmetric metric connection that satisfies several relations on 1–form, differential equations, recurrent space, and Einstein manifold. In this paper, we also study weakly symmetric Kähler manifolds with parallel Weyl conformal curvature tensor on weakly symmetric Kähler manifolds with a special type of semi-symmetric metric connection and have shown that it is an Einstein manifold and it is reduced to a recurrent space.

The objective of this paper is to explore the complete lifts of a quarter-symmetric metric connection from a Sasakian manifold to its tangent bundle. A relationship between the Riemannian connection and the quarter-symmetric metric connection from a Sasakian manifold to its tangent bundle was established. Some theorems on the curvature tensor and the projective curvature tensor of a Sasakian manifold with respect to the quarter-symmetric metric connection to its tangent bundle were proved. Finally, locally ϕ-symmetric Sasakian manifolds with respect to the quarter-symmetric metric connection to its tangent bundle were studied.

The purpose of the present paper is to study some properties of generalized M -projective curvature tensor of a para-Sasakian manifold admitting Zamkovoy connection. The generalized M -projective is obtained with the help of a new generalized (0,2) symmetric tensor Z introduced by Mantica and Suh [10]. It is shown that para-Sasakian manifold satisfying the condition R ( X , Y ) ⋅ M ~ ∗∗ = 0 is an η -Einstein manifold. Also, we found that a para-Sasakian manifold satisfying M ~ ∗∗ ( X , Y ) ⋅ S = 0 is either an Einstein manifold or ψ = 1 on it.