• Honam Mathematical Journal
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• v.46 no.3
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• pp.393-406
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• 2024

In the present paper, we classify the Ricci solitons and the Ricci bi-conformal vector fields on the model space Sol⁴₁. Also, we show that which of them are gradient vector fields and Killing vector fields.

• Journal of the Korean Mathematical Society
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• v.44 no.3
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• pp.605-613
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• 2007

Main interest of the present paper is to investigate the criticality of characteristic vector fields on almost cosymplectic manifolds. Killing critical characteristic vector fields are absolute minima. This paper contains some examples of non-Killing critical characteristic vector fields.

• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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• pp.1339-1350
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• 2018

We will find a necessary and sufficient condition for unit Killing vector fields to be minimal and provide an application of the obtained result.

• Journal of the Korean Mathematical Society
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• v.57 no.2
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• pp.523-537
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• 2020

In this work we consider the Sol₃ Lie group, equipped with the left-invariant metric, Lorentzian or Riemannian. We determine Killing vector fields and affine vectors fields. Also we obtain a full classification of Ricci, curvature and matter collineations.

• Bulletin of the Korean Mathematical Society
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• v.57 no.5
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• pp.1299-1306
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• 2020

An almost contact metric manifold is called a quasi contact metric manifold if the corresponding almost Hermitian cone is a quasi Kähler manifold, which was introduced by Y. Tashiro [9] as a contact O*-manifold. In this paper, we show that a quasi contact metric manifold with Killing characteristic vector field is a K-contact manifold. This provides an extension of the definition of K-contact manifold.

• Journal of the Korean Mathematical Society
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• v.55 no.1
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• pp.1-16
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• 2018

In this paper, we give characteristic differential equations of a kind of projective vector fields on Finsler manifolds. Using these equations, we prove the vanishing theorem of projective vector fields on any compact Finsler manifold with the negative mean Ricci curvature, which is defined in [10]. This result involves the vanishing theorem of Killing vector fields in the Riemannian case and the work of [1, 14].

• Honam Mathematical Journal
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• v.45 no.2
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• pp.316-324
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• 2023

The P-curvature tensor has been studied in the space-time of general relativity and it is found that the contracted part of this tensor vanishes in the Einstein space. It is shown that Rainich conditions for the existence of non-null electro variance can be obtained by P_𝛼𝛽. It is established that the divergence of tensor G_𝛼𝛽 defined with the help of P_𝛼𝛽 and scalar P is zero, so that it can be used to represent Einstein field equations. It is shown that for V₄ satisfying Einstein like field equations, the tensor P_𝛼𝛽 is conserved, if the energy momentum tensor is Codazzi type. The space-time satisfying Einstein's field equations with vanishing of P-curvature tensor have been considered and existence of Killing, conformal Killing vector fields and perfect fluid space-time has been established.

• Communications of the Korean Mathematical Society
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• v.13 no.4
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• pp.817-823
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• 1998

In the present paper, we study conformal and projective Killing vector fields and infinitesimal Q-transformations on a quaternionic Kahlerian manifold, and prove that an infinitesimal conformal or projective automorphism in a compact quaternionic Kahlerian manifold is necessarily infinitesimal automorphism.

• Journal of the Korean Mathematical Society
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• v.14 no.1
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• pp.135-142
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• 1977

• Journal of the Korean Mathematical Society
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• v.18 no.1
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• pp.73-80
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• 1981