• Journal of the Korean Mathematical Society
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• v.57 no.4
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• pp.1005-1018
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• 2020

A characterization of the C-projective vector fields on a Randers space is presented in terms of 𝚵-curvature. It is proved that the 𝚵-curvature is invariant for C-projective vector fields. The dimension of the algebra of the C-projective vector fields on an n-dimensional Randers space is at most n(n + 2). The generalized Funk metrics on the n-dimensional Euclidean unit ball 𝔹ⁿ(1) are shown to be explicit examples of the Randers metrics with a C-projective algebra of maximum dimension n(n+2). Then, it is also proved that an n-dimensional Randers space has a C-projective algebra of maximum dimension n(n + 2) if and only if it is locally Minkowskian or (up to re-scaling) locally isometric to the generalized Funk metric. A new projective invariant is also introduced.

• Journal of the Korean Mathematical Society
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• v.55 no.2
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• pp.391-413
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• 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 $(PSPS)_4$.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.1
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• pp.87-95
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• 2019

The homothety classes of lattices in a two dimensional vector space over a nonarchimedean local field form a regular tree ${\mathcal{T}}$ of degree q + 1 on which the projective linear group acts naturally where q is the order of the residue field. We show that for any finite regular combinatorial graph of even degree q + 1, there exists a torsion free discrete subgroup ${\Gamma}$ of the projective linear group such that ${\mathcal{T}}/{\Gamma}$ is isomorphic to the graph.

• Communications of the Korean Mathematical Society
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• v.12 no.4
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• pp.1007-1013
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• 1997

The purposer of this paper is to prove a rigidity theorem for real hypersurfaces in a complex projective spece.

• Journal of applied mathematics & informatics
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• v.41 no.5
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• pp.989-999
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• 2023

The aim of this paper is to study the projective curvature tensor field of the Curvature tensor Rⁱ_jkh on a recurrent non Riemannian space admitting recurrent affine motion, which is also decomposable in the form Rⁱ_jkh=Xⁱ Y_jkh, where Xⁱ and Y_jkh are non-null vector and tensor respectively. In this paper we decompose Special Pseudo Projective Curvature Tensor Field. In the sequal of decomposition we established several properties of such decomposed tensor fields. We have considered the curvature tensor field Rⁱ_jkh in a Finsler space equipped with non symmetric connection and we study the decomposition of such field. In a special Pseudo recurrent Finsler Space, if the arbitrary tensor field 𝜓ⁱ_j is assumed to be a covariant constant then, in view of the decomposition rule, 𝜙_kh behaves as a recurrent tensor field. In the last, we have considered the decomposition of curvature tensor fields in Kaehlerian recurrent spaces and have obtained several related theorems.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.571-580
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• 2018

The object of the present paper is to prove the non-existence of pseudo projective Ricci symmetric spacetimes $(PW\;RS)_4$ with different types of energy momentum tensor. We also discuss whether a fluid $(PW\;RS)_4$ spacetime with the basic vector field as the velocity vector field of the fluid can admit heat flux. Next we consider perfect fluid and dust fluid $(PW\;RS)_4$ spacetimes respectively. Finally we construct an example of a $(PW\;RS)_4$ spacetime.

• Communications of the Korean Mathematical Society
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• v.18 no.2
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• pp.309-323
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• 2003

In this paper, We characterize a semi-invariant sub-manifold of codimension 3 satisfying ∇$\varepsilon$A = 0 in a complex projective space CP$\^$n+1/, where ∇$\varepsilon$A is the covariant derivative of the shape operator A in the direction of the distinguished normal with respect to the structure vector field $\varepsilon$.

• Kyungpook Mathematical Journal
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• v.46 no.4
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• pp.463-476
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• 2006

It is known that there are no real hypersurfaces with parallel Ricci tensor in a nonflat complex space form ([6], [9]). In this paper we investigate real hypersurfaces in a complex projective space $P_n\mathbb{C}$ using some conditions of the Ricci tensor S which are weaker than ${\nabla}S=0$. We characterize Hopf hypersurfaces of $P_n\mathbb{C}$.

• Honam Mathematical Journal
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• v.24 no.1
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• pp.109-119
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• 2002

Some sufficient conditions on the existence and uniqueness of certain symmetric balanced incomplete block design are introduced. Also, a construction algorithm for the design and some examples are presented. The algorithm is developed based on the construction of subspaces of the three-dimensional vector space over a field.

• Bulletin of the Korean Mathematical Society
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• v.29 no.1
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• pp.73-80
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• 1992

We discuss transverse harmonic fields on compact foliated Riemannian manifolds, and give a necessary and sufficient condition for a transverse field to be a transverse harmonic one and the non-existence of transverse harmonic fields. 1. On a foliated Riemannian manifold, geometric transverse fields, that is, transverse Killing, affine, projective, conformal fields were discussed by Kamber and Tondeur([3]), Molino ([5], [6]), Pak and Yorozu ([7]) and others. If the foliation is one by points, then transverse fields are usual fields on Riemannian manifolds. Thus it is natural to extend well known results concerning those fields on Riemannian manifolds to foliated cases. On the other hand, the following theorem is well known ([1], [10]): If the Ricci operator in a compact Riemannian manifold M is non-negative everywhere, then a harmonic vector field in M has a vanishing covariant derivative. If the Ricci operator in M is positive-definite, then a harmonic vector field other than zero does not exist in M.