The object of the present paper is to prove that in a quasi-Sasakian\n 3-manifold admitting ?-Ricci soliton, the structure function ? is a\n constant. As a consequence we obtain several important results.

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On quasi-Sasakian 3-manifolds admitting η-Ricci solitons

Abstract In this paper we study η-Ricci solitons on Sasakian 3-manifolds. Among others we prove that an η-Ricci soliton on a Sasakian 3-manifold is an η-Einstien manifold. Moreover we consider η-Ricci solitons on Sasakian 3-manifolds with Ricci tensor of Codazzi type and cyclic parallel Ricci tensor. Beside these we study conformally flat and φ-Ricci symmetric η-Ricci soliton on Sasakian 3-manifolds. Also η-Ricci soliton on Sasakian 3-manifolds with the curvature condition Q.R = 0 have been considered. Finally, we construct an example to prove the non-existence of proper η-Ricci solitons on Sasakian 3-manifolds and verify some results.

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-Ricci Solitons on Sasakian 3-Manifolds

In this paper we study a special type of metric called *-Ricci soliton on para-Sasakian manifold. We prove that if the para-Sasakian metric is a *-Ricci soliton on a manifold M, then M is either D-homothetic to an Einstein manifold, or the Ricci tensor of M with respect to the canonical paracontact connection vanishes.

Para-Sasakian manifolds and *-Ricci solitons

Ricci-like solitons with arbitrary potential are introduced and studied on Sasaki-like almost contact B-metric manifolds. It is proved that the Ricci tensor of such a soliton is the vertical component of both B-metrics multiplied by a constant. It is established that gradient almost Ricci-like solitons have constant soliton coefficients. Explicit examples of Lie groups as manifolds of dimensions 3 and 5 equipped with the structures studied are provided.

Ricci-like solitons with arbitrary potential and gradient almost Ricci-like solitons on Sasaki-like almost contact B-metric manifolds

Abstract In the present paper we study η-Ricci solitons on Kenmotsu 3-manifolds. Moreover, we consider η-Ricci solitons on Kenmotsu 3-manifolds with Codazzi type of Ricci tensor and cyclic parallel Ricci tensor. Beside these, we study φ-Ricci symmetric η-Ricci soliton on Kenmotsu 3-manifolds. Also Kenmotsu 3-manifolds satisfying the curvature condition R.R = Q(S, R)is considered. Finally, an example is constructed to prove the existence of a proper η-Ricci soliton on a Kenmotsu 3-manifold.

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η-Ricci Solitons on Kenmotsu 3-Manifolds

The present paper aims at studying a Ricci solitons on para-Sasakian manifolds. We give the results on Ricci solitons in para-Sasakian manifold satisfying the conditions 0 = ) , ( R X S   , 0 = ) , ( P X R   and 0 = ) , ( H X R   ,where P , H are pseudo-projective and quasi-conharmonic curvature tensors, respectively. MSC(2000): 53C21; 53C44; 53C25.

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Balachandra S. Hadimani

Papers

Ricci Solitons on Para-Sasakian Manifolds