• East Asian mathematical journal
• /
• v.38 no.5
• /
• pp.549-581
• /
• 2022

Let M be a semi-invariant submanifold with almost contact metric structure (𝜙, 𝜉, 𝜂, g) of codimension 3 in a complex space form M_n+1(c), c≠ 0. We denote by S and R_𝜉 be the Ricci tensor of M and the structure Jacobi operator in the direction of the structure vector 𝜉, respectively. Suppose that the third fundamental form t satisfies dt(X, Y) = 2𝜃g(𝜙X, Y) for a certain scalar 𝜃(≠ 2c) and any vector fields X and Y on M. In this paper, we prove that M satisfies R_𝜉S = SR_𝜉 and at the same time R_𝜉𝜙 = 𝜙R_𝜉, then M is a Hopf hypersurface of type (A) provided that the scalar curvature s of M holds s - 2(n - 1)c ≤ 0.

• Kyungpook Mathematical Journal
• /
• v.62 no.1
• /
• pp.133-166
• /
• 2022

Let M be a semi-invariant submanifold with almost contact metric structure (𝜙, 𝜉, 𝜂, g) of codimension 3 in a complex space form M_n+1(c) for c ≠ 0. We denote by S and R_𝜉 be the Ricci tensor of M and the structure Jacobi operator in the direction of the structure vector 𝜉, respectively. Suppose that the third fundamental form t satisfies dt(X, Y) = 2𝜃g(𝜙X, Y) for a certain scalar 𝜃 ≠ 2c and any vector fields X and Y on M. In this paper, we prove that if it satisfies R_𝜉𝜙 = 𝜙R_𝜉 and at the same time S𝜉 = g(S𝜉, 𝜉)𝜉, then M is a real hypersurface in M_n(c) (⊂ M_n+1(c)) provided that $\bar{r}-2(n-1)c{\leq}0$, where $\bar{r}$ denotes the scalar curvature of M.

• Journal of the Korean Mathematical Society
• /
• v.16 no.2
• /
• pp.137-153
• /
• 1980

• Journal of applied mathematics & informatics
• /
• v.5 no.2
• /
• pp.547-551
• /
• 1998

We give some examples of extremal minimal free reso-lutions of Gorenstein ideals of codimension 4.

• Journal of applied mathematics & informatics
• /
• v.13 no.1_2
• /
• pp.405-411
• /
• 2003

We prove that 25 different Artinian O-Sequences of codimension 3 type 3 with length 7 among all possible 334 cases are not level.

• East Asian mathematical journal
• /
• v.14 no.2
• /
• pp.269-279
• /
• 1998

For a codimension 1 submanifold in a Euclidean 2n-space, the degree of the gauss map mod 2 is the semi-characteristic of the manifold in $Z_2$ coefficient.

• Honam Mathematical Journal
• /
• v.27 no.4
• /
• pp.631-639
• /
• 2005

For compact Hausdorff spaces X and Y let C(X) and C(Y) denote the complex Banach spaces of complex valued continuous functions on X and Y, respectively. Also let $T:C(X){\rightarrow}C(Y)$ be a linear isomerty. Necessary and sufficient conditions are given such that range of T has finite codimension.

• Communications of the Korean Mathematical Society
• /
• v.12 no.3
• /
• pp.685-690
• /
• 1997

Our study focuses on the condition under which a subspace of complex projective space can become an Einstein space. We prove that a subspace becomes an Einstein space if it's codimension is less than n-1 and its curvature tensor and Ricci tensor satisfies Ryan's condition.

• Journal of applied mathematics & informatics
• /
• v.13 no.1_2
• /
• pp.433-440
• /
• 2003

Artinian O-sequences of codimension 3 and type 3 with length 7 are classified as level or non-level. Some cases are proved to be non-level among the 334 cases which have been suspected to be level.

• Journal of applied mathematics & informatics
• /
• v.22 no.1_2
• /
• pp.563-568
• /
• 2006

We introduce how to construct a non-unimodal level O-sequence which has all different local maxima as many as we desire.