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기우항,송현정 영남수학회 2024 East Asian mathematical journal Vol.40 No.1
Let $M$ be a semi-invariant submanifold of codimension 3with almost contact metric structure $(\phi, \xi, \eta, g)$ in a complex space form$M_{n+1} (c)$. We denote by $A$, $K$ and $L$ the second fundamental forms with respect to theunit normal vector $C$, $D$ and $E$ respectively, where $C$ is the distinguished normal vector,and by $R_\xi=R(\xi,\cdot)\xi$ the structure Jacobi operator. Suppose that the third fundamental form $t$ satisfies $dt(X,Y)=2\theta g(\phi X,Y)$ for a scalar$\theta(\neq2c)$ and any vector fields $X$ and $Y$, and at the same time $R_\xi K=KR_\xi$ and$\nabla_{\phi\nabla_{\xi}\xi}R_\xi=0$. In this paper, we prove thatif it satisfies $\nabla_\xi R_\xi =0$ on $M$, then $M$ is a real hypersurface of type ($A$) in$M_{n} (c)$ provided that the scalar curvature $\bar{r}$ of $M$ holds $\bar{r}-2(n-1)c\leq0$.
Jacobi operators along the structure flow on real hypersurfaces in a nonflat complex space form II
기우항,Hiroyuki Kurihara 대한수학회 2011 대한수학회보 Vol.48 No.6
Let M be a real hypersurface of a complex space form with almost contact metric structure (ø, ξ, ŋ, g). In this paper, we study real hypersurfaces in a complex space form whose structure Jacobi operator R_ξ=R(· , ξ)ξ is ξ-parallel. In particular, we prove that the condition ∇_ξR_ξ=0 characterizes the homogeneous real hypersurfaces of type A in a complex projective space or a complex hyperbolic space when R_ξØS=R_ξSØ holds on M, where S denotes the Ricci tensor of type (1,1) on M.
기우항 慶北大學校 科學敎育硏究所 2004 科學敎育硏究誌 Vol.28 No.-
Geometry has the oldest root in the history of mathematics. Geometry started from Euclidean geometry and the Euclidean geometry is based on the axiom of the parallel lines. In this article we overview the advent of other geometries such as parabolic geometry and hyperbolic geometry and see that there could be plenty of geometries in which two parallel lines may or may not meet.
Structure Jacobi Operator of Semi-invarinat Submanifolds in Complex Space Forms
기우항,김수진 영남수학회 2020 East Asian mathematical journal Vol.36 No.3
Let M be a semi-invariant submanifold of codimension 3 with almost contact metric structure (φ, ξ, η, g) in a complex space form Mn+1(c), c ̸= 0. We denote by Rξ and RX′ be the structure Jacobi operator with re- spect to the structure vector ξ and be RX′ = (∇XR)(·,X)X for any unit vector field X on M, respectively. Suppose that the third fundamental form t satisfies dt(X, Y ) = 2θg(φX, Y ) for a scalar θ(̸= 2c) and any vector fields X and Y on M. In this paper, we prove that if it satisfies Rξφ = φRξ and at the same time Rξ′ = 0, then M is a Hopf real hypersurfaces of type (A), provided that the scalar curvature r ̄ of M holds r ̄ − 2(n − 1)c ≤ 0.
Certain Characterization of Real Hypersurfaces of type A in a Nonflat Complex Space Form
기우항 경북대학교 자연과학대학 수학과 2021 Kyungpook mathematical journal Vol.61 No.1
Let M be a real hypersurface with almost contact metric structure (φ, ξ, η, g) in a nonflat complex space form Mn(c). We denote S and Rξ by the Ricci tensor of M and by the structure Jacobi operator with respect to the vector field ξ respectively. In this paper, we prove that M is a Hopf hypersurface of type A in Mn(c) if it satisfies Rξφ = φRξ and at the same time Rξ(Sφ − φS) = 0.
CHARACTERIZATIONS OF REAL HYPERSURFACES OF TYPE A IN A COMPLEX SPACE FORM
기우항,김인배,임동호 대한수학회 2010 대한수학회보 Vol.47 No.1
Let M be a real hypersurface with almost contact metric structure (Φ, g, ξ,η) in a complex space form Mn(c), c≠0. In this paper we prove that if RξLξg = 0 holds on M, then M is a Hopf hypersurface in Mn(c), where Rξ and Lξ denote the structure Jacobi operator and the operator of the Lie derivative with respect to the structure vector field ξ respectively. We characterize such Hopf hypersurfaces of Mn(c).
기우항,김영호,이윤종,정원우,김민숙 경북대학교 과학교육연구소 1997 科學敎育硏究誌 Vol.21 No.-
The purpose of this study is to compare and analyze the eight current mathematics textbooks in order to them effectively in the course of instruction according to the result. Basically the study has been carried out to compare and analyze what is the difference between the current curriculum and the last one, and the development of the teaching procedure, the difference of the quality and contents in the eight kind of text books.
Structure Jacobi Operators of Semi-invarinat Submanifolds in a Complex Space Form II
기우항,김수진 영남수학회 2022 East Asian mathematical journal Vol.38 No.1
Let $M$ be a semi-invariant submanifold of codimension 3 with almost contact metric structure$(\phi, \xi, \eta, g)$ in a complex space form $M_{n+1} (c)$. We denote by $R_\xi$ the structureJacobi operator with respect to the structure vector field $\xi$ and by $\bar{r}$ the scalar curvature of $M$. Suppose that $R_\xi$ is $\phi\nabla_\xi \xi$-parallel and at the same time the third fundamental form$t$ satisfies $dt(X,Y)=2\theta g(\phi X,Y)$ for a scalar $\theta(\neq2c)$ and any vector fields$X$ and $Y$ on $M$. In this paper, we prove that if it satisfies $R_\xi \phi=\phi R_\xi$, then $M$ is a Hopf hypersurfaceof type (A) in $M_{n+1} (c)$ provided that $\bar{r}-2(n-1)c\leq0$.