• Kyungpook Mathematical Journal
• /
• v.56 no.3
• /
• pp.951-964
• /
• 2016

The objective of the present paper is to study some new results on concircular curvature tensor in a Kenmotsu manifold with respect to the semi-symmetric non-metric connection.

• Journal of the Chungcheong Mathematical Society
• /
• v.24 no.4
• /
• pp.825-832
• /
• 2011

In this paper, we make a minute and detailed proof of a part which is omitted in the process of obtaining the value of the curvature tensor for an invariant affine connection at the point {H} of a reductive homogeneous space G/H in the paper 'Invariant affine connections on homogeneous spaces' by K. Nomizu.

• Bulletin of the Korean Mathematical Society
• /
• v.56 no.5
• /
• pp.1341-1353
• /
• 2019

For complete Riemannian manifolds with vanishing Bach tensor and positive constant scalar curvature, we provide a rigidity theorem characterized by some pointwise inequalities. Furthermore, we prove some rigidity results under an inequality involving $L^{\frac{n}{2}}$-norm of the Weyl curvature, the traceless Ricci curvature and the Sobolev constant.

• Honam Mathematical Journal
• /
• v.40 no.3
• /
• pp.487-508
• /
• 2018

In this study, we use the generalized Tanaka-Webster connection on a trans-Sasakian manifold of type (${\alpha},{\beta}$) and obtain the curvature tensors of a trans-Sasakian manifold with respect to this connection. Also, we investigate some special curvature conditions of a trans-Sasakian manifold with respect to generalized Tanaka-Webster connection and finally, give an example for trans-Sasakian manifolds.

• Honam Mathematical Journal
• /
• v.40 no.2
• /
• pp.325-346
• /
• 2018

The object of the present paper is to study some types of Ricci pseudosymmetric $(LCS)_n$-manifolds whose metric is Ricci soliton. We found the conditions when Ricci soliton on concircular Ricci pseudosymmetric, projective Ricci pseudosymmetric, $W_3$-Ricci pseudosymmetric, conharmonic Ricci pseudosymmetric, conformal Ricci pseudosymmetric $(LCS)_n$-manifolds to be shrinking, steady and expanding. We also construct an example of concircular Ricci pseudosymmetric $(LCS)_3$-manifold whose metric is Ricci soliton.

• Journal of the Korean Mathematical Society
• /
• v.55 no.2
• /
• pp.391-413
• /
• 2018

In this paper we introduce a new tensor named semi-projective curvature tensor which generalizes the projective curvature tensor. First we deduce some basic geometric properties of semi-projective curvature tensor. Then we study pseudo semi-projective symmetric manifolds $(PSPS)_n$ which recover some known results of Chaki [5]. We provide several interesting results. Among others we prove that in a $(PSPS)_n$ if the associated vector field ${\rho}$ is a unit parallel vector field, then either the manifold reduces to a pseudosymmetric manifold or pseudo projective symmetric manifold. Moreover we deal with semi-projectively flat perfect fluid and dust fluid spacetimes respectively. As a consequence we obtain some important theorems. Next we consider the decomposability of $(PSPS)_n$. Finally, we construct a non-trivial Lorentzian metric of $(PSPS)_4$.

• Communications of the Korean Mathematical Society
• /
• v.38 no.3
• /
• pp.837-846
• /
• 2023

In this paper, we firstly construct a Hsu-B manifold and give some basic results related to it. Then, we address a semi-symmetric metric F-connection on the Hsu-B manifold and obtain the curvature tensor fields of such connection, and study properties of its curvature tensor and torsion tensor fields.

• Korean Journal of Mathematics
• /
• v.19 no.1
• /
• pp.25-32
• /
• 2011

This paper is a direct continuation of [1]. In this paper we investigate some properties of ES-curvature tensor of g - $ESX_n$, with main emphasis on the derivation of several useful generalized identities involving it. In this subsequent paper, we are concerned with contracted curvature tensors of g - $ESX_n$ and several generalized identities involving them. In particular, we prove the first variation of the generalized Bianchi's identity in g - $ESX_n$, which has a great deal of useful physical applications.

• Communications of the Korean Mathematical Society
• /
• v.34 no.3
• /
• pp.881-896
• /
• 2019

In the present paper, we study certain curvature conditions satisfying by the projective curvature tensor in Sasakian manifolds with respect to the generalized-Tanaka-Webster connection. Finally, we give an example of a 3-dimensional Sasakian manifold with respect to the generalized-Tanaka-Webster connection.

• Journal of the Chungcheong Mathematical Society
• /
• v.32 no.3
• /
• pp.281-293
• /
• 2019

In the present paper, we study quasi-concircular curvature tensor satisfying certain curvature conditions on a Lorentzian ${\beta}$-Kenmotsu manifold with respect to the semi-symmetric semi-metric connection.