Ricci and scalar curvatures of submanifolds of a conformal Sasakian space form (original) (raw)

Ricci curvature of submanifolds in Sasakian space forms

International Journal of Mathematics and Mathematical Sciences, 2002

Recently, Chen established a sharp relationship between the Ricci curvature and the squared mean curvature for a submanifold in a Riemannian space form with arbitrary codimension. Afterwards, we dealt with similar problems for submanifolds in complex space forms.

A lower bound for the Ricci curvature of submanifolds in generalized Sasakian space forms

Abstract. In this paper, we obtain inequalities between the Ricci curvature, the scalar curvature and the squared mean curvature of submanifolds in generalized Sasakian space forms such that each inequality is a lower bound for the Ricci curvature. Also, we obtain a sharp relationship between the scalar curvature, a Riemannian invariant and the squared mean curvature of anti-invariant submanifolds in generalized Sasakian space forms.

Quasi-Conformal Curvature Tensor of Generalized Sasakian-Space-Forms

Facta Universitatis, Series: Mathematics and Informatics, 2020

The present paper deals the study of generalised Sasakian-space-forms with the conditions Cq(ξ,X).S = 0, Cq(ξ,X).R = 0 and Cq(ξ,X).Cq = 0, where R, S and Cq denote Riemannian curvature tensor, Ricci tensor and quasi-conformal curvature tensor of the space-form, respectively and at last, we have given some examples to improve our results.

Some curvature properties of trans-Sasakian manifolds

Lobachevskii Journal of Mathematics, 2014

The object of the present paper is to study quasi-conformally flat trans-Sasakian manifolds. We consider trans-Sasakian manifolds with η-parallel and cyclic parallel Ricci tensors. φ-Ricci symmetric quasi-conformally flat trans-Sasakian manifolds have been studied. We also investigates quasi-conformally flat trans-Sasakian manifolds which are Einstein Semi-symmetric.

Ricci Soliton and Certain Related Metrics on a Three-Dimensional Trans-Sasakian Manifold

Universe

In this article, a Ricci soliton and *-conformal Ricci soliton are examined in the framework of trans-Sasakian three-manifold. In the beginning of the paper, it is shown that a three-dimensional trans-Sasakian manifold of type (α,β) admits a Ricci soliton where the covariant derivative of potential vector field V in the direction of unit vector field ξ is orthogonal to ξ. It is also demonstrated that if the structure functions meet α2=β2, then the covariant derivative of V in the direction of ξ is a constant multiple of ξ. Furthermore, the nature of scalar curvature is evolved when the manifold of type (α,β) satisfies *-conformal Ricci soliton, provided α≠0. Finally, an example is presented to verify the findings.

Conformal Ricci Soliton in Lorentzian α-Sasakian Manifolds

2017

In this paper we have studied conformal curvature tensor, conharmonic curvature tensor, projective curvature tensor in Lorentzian α-Sasakian manifolds admitting conformal Ricci soliton. We have found that a Weyl conformally semi symmetric Lorentzian α-Sasakian manifold admitting conformal Ricci soliton is η-Einstein manifold. We have also studied conharmonically Ricci symmetric Lorentzian α-Sasakian manifold admitting conformal Ricci soliton. Similarly we have proved that a Lorentzian αSasakian manifold M with projective curvature tensor admitting conformal Ricci soliton is η-Einstein manifold. We have also established an example of 3-dimensional Lorentzian α-Sasakian manifold.

Ricci curvature of submanifolds in Kenmotsu space forms

International Journal of Mathematics and Mathematical Sciences, 2002

In 1999, Chen established a sharp relationship between the Ricci curvature and the squared mean curvature for a submanifold in a Riemannian space form with arbitrary codimension. Similar problems for submanifolds in complex space forms were studied by Matsumoto et al. In this paper, we obtain sharp relationships between the Ricci curvature and the squared mean curvature for submanifolds in Kenmotsu space forms.

On the Ricci Tensor of Submanifolds in Conformal Kenmotsu Manifolds

Kyushu Journal of Mathematics, 2017

In this paper, we obtain several interesting results on submanifolds of conformal Kenmotsu manifolds. In addition to this we consider submanifolds of a conformal Kenmotsu manifold of which the Ricci tensor is parallel, Lie ξ-parallel or recurrent. We also present an illustration example of a three-dimensional conformal Kenmotsu manifold that is not Kenmotsu.