• 대한수학회지
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• 제45권2호
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• pp.367-376
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• 2008

The main purpose of this paper is to investigate diagonal lift of tensor fields of type (1,1) from manifold to its tensor bundle of type (p, q) and to prove that when a manifold $M_n$ admits a $K\ddot{a}hlerian$ structure ($\varphi$,g), its tensor bundle of type (p,q) admits an complex structure.

• 호남수학학술지
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• 제42권1호
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• pp.63-74
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• 2020

In this paper firstly, Some properties were given about metallic Riemannian structure on (1, 1)-tensor bundle. Secondly, the Tachibana and Vishnevskii operators were applied to vertical and horizontal lifts with respect to the metallic Riemannian structure on (1, 1)-tensor bundle, respectively.

• 대한수학회지
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• 제61권2호
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• pp.255-277
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• 2024

In this paper, we introduce the notion of stress-energy tensor Q of the traceless Ricci tensor for Riemannian manifolds (Mⁿ, g), and investigate harmonicity of Riemannian curvature tensor and Weyl curvature tensor when (M, g) satisfies some geometric structure such as critical point equation or vacuum static equation for smooth functions.

• 호남수학학술지
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• 제32권4호
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• pp.747-761
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• 2010

It is known that there are no real hypersurfaces with parallel structure Jacobi operator $R_{\xi}$ (cf.[16], [17]). In this paper we investigate real hypersurfaces in a nonflat complex space form using some conditions of the structure Jacobi operator $R_{\xi}$ which are weaker than ${\nabla}R_{\xi}$ = 0. Under further condition $S\phi={\phi}S$ for the Ricci tensor S we characterize Hopf hypersurfaces in a complex space form.

• Kyungpook Mathematical Journal
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• 제46권4호
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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 $P_n\mathbb{C}$.

• 대한수학회보
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• 제42권1호
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• pp.93-119
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• 2005

In this paper, we characterize some semi-invariant sub-manifolds of codimension 3 with almost contact metric structure ($\phi$, $\xi$, g) in a complex projective space $CP^{n+1}$ in terms of the structure tensor $\phi$, the Ricci tensor S and the Jacobi operator $R_\xi$ with respect to the structure vector $\xi$.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제28권1호
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• pp.55-60
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• 2021

Let M be a real hypersurface in a complex space form Mn(c), c ≠ 0. In this paper we prove that if the structure tensor field is Codazzi type, then M is a Hopf hypersurface. We characterize such Hopf hypersurfaces of Mn(c).

• 대한수학회지
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• 제44권2호
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• pp.307-326
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• 2007

We know that there are no real hypersurfaces with parallel Ricci tensor or parallel structure Jacobi operator in a nonflat complex space form (See [4], [6], [10] and [11]). In this paper we investigate real hypersurfaces M in a nonflat complex space form $M_n(c)$ under the condition that ${\nabla}_{\varepsilon}S=0\;and\;{\nabla}_{\varepsilon}R_{\varepsilon}=0,\;where\;S\;and\;R_{\varepsilon}$ respectively denote the Ricci tensor and the structure Jacobi operator of M in $M_n(c)$.

• Kyungpook Mathematical Journal
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• 제59권1호
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• pp.149-161
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• 2019

In the present paper, we study curvature properties of ${\eta}$-Ricci solitons on para-Kenmotsu manifolds. We obtain some results of ${\eta}$-Ricci solitons on para-Kenmotsu manifolds satisfying $R({\xi},X).C=0$, $R({\xi},X).{\tilde{M}}=0$, $R({\xi},X).P=0$, $R({\xi},X).{\tilde{C}}=0$ and $R({\xi},X).H=0$, where $C,\;{\tilde{M}},\;P,\;{\tilde{C}}$ and H are a quasi-conformal curvature tensor, a M-projective curvature tensor, a pseudo-projective curvature tensor, and a concircular curvature tensor and conharmonic curvature tensor, respectively.

• 대한수학회논문집
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• 제9권2호
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• pp.393-400
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• 1994

Let M(f,η,ξ,g) be a (2m ＋ 1)-dimensional Sasakian manifold with soldering form dp ∈ ΓHom(Λ/sup q/TM, TM) (dp: canonical vector-valued 1-form) where f,η,ξ and g are the (1,1)-tensor field, the structure 1-form, the structure vector field and the metric tensor of M, respectively.(omitted)