• Bulletin of the Korean Mathematical Society
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• v.34 no.2
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• pp.173-184
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• 1997

An n-dimensional complex space form $M_n(c)$ is a Kaehlerian manifold of constant holomorphic sectional curvature c. As is well known, complete and simply connected complex space forms are a complex projective space $P_n C$, a complex Euclidean space $C_n$ or a complex hyperbolic space $H_n C$ according as c > 0, c = 0 or c < 0.

• Communications of the Korean Mathematical Society
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• v.36 no.2
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• pp.377-387
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• 2021

In the present paper, we characterize quasi-Sasakian 3-manifolds admitting 𝜂-Ricci solitons. Finally, the existence of 𝜂-Ricci soliton in a quasi-Sasakian 3-manifold has been proved by a concrete example.

• Journal of the Korean Mathematical Society
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• v.57 no.4
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• pp.873-892
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• 2020

Thurston, in 1986, discovered that the Schwarzian derivative has mysterious properties similar to the curvature on a manifold. After his work, there are several approaches to develop this notion on Riemannian manifolds. Here, a tensor field is identified in the study of global conformal diffeomorphisms on Finsler manifolds as a natural generalization of the Schwarzian derivative. Then, a natural definition of a Mobius mapping on Finsler manifolds is given and its properties are studied. In particular, it is shown that Mobius mappings are mappings that preserve circles and vice versa. Therefore, if a forward geodesically complete Finsler manifold admits a Mobius mapping, then the indicatrix is conformally diffeomorphic to the Euclidean sphere S^n-1 in ℝⁿ. In addition, if a forward geodesically complete absolutely homogeneous Finsler manifold of scalar flag curvature admits a non-trivial change of Mobius mapping, then it is a Riemannian manifold of constant sectional curvature.

• Communications of the Korean Mathematical Society
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• v.29 no.2
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• pp.331-343
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• 2014

The object of the present paper is to study a semi-symmetric metric connection in an (${\varepsilon}$)-Kenmotsu manifold. In this paper, we study a semi-symmetric metric connection in an (${\varepsilon}$)-Kenmotsu manifold whose projective curvature tensor satisfies certain curvature conditions.