• 대한수학회보
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• 제59권6호
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• pp.1595-1603
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• 2022

We show how some of well-known recurrent operators such as recurrent curvature operator, recurrent Ricci operator, recurrent Jacobi operator, recurrent shape and Weyl operators have the significant role for biharmonic hypersurfaces to be minimal in the Euclidean space.

• Kyungpook Mathematical Journal
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• 제57권3호
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• pp.525-535
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• 2017

In this paper, we consider two kinds of derivatives for the shape operator of a real hypersurface in a $K{\ddot{a}}hler$ manifold which are named the Lie derivative and the covariant derivative with respect to the k-th generalized Tanaka-Webster connection ${\hat{\nabla}}^{(k)}$. The purpose of this paper is to study Hopf hypersurfaces in complex Grassmannians of rank two, whose Lie derivative of the shape operator coincides with the covariant derivative of it with respect to ${\hat{\nabla}}^{(k)}$ either in direction of any vector field or in direction of Reeb vector field.

• 전자공학회논문지C
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• 제34C권4호
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• pp.36-44
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• 1997

An efficient context-free multiple-object segmentation using attention operator based on modified generalized symmetry transform is proposed and implemented by modifying a radial basis function network. By using the difference of intensity gradient, instead of te intensity gradient itself, in generalized symmetry tranform so as to make the attention operator to preserve the edges of the objects shape, an efficient context-free multiple-object segementation is proposed in which no a priori shape informtion on the objects is requried. The attention operator is implemented by using a modified radial basis function network which can reflect symmetry, and by using te edge pyramid of the input image, both of the local and the global symmetry of the objects are reflected simultaneously to make the multiple-object with different sizes be segmented with a singel fixed-size $n\timesm$ can be done with O(n) complexity. The simulaton results show that the proposed algorithm can efficiently be used in context-free multiple-object segmentation even for the low contrast IR images as well as for the images from the camera.

• 대한수학회보
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• 제52권5호
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• pp.1621-1630
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• 2015

In this paper the notion of Lie derivative of a tensor field T of type (1,1) of real hypersurfaces in complex space forms with respect to the generalized Tanaka-Webster connection is introduced and is called generalized Tanaka-Webster Lie derivative. Furthermore, three dimensional real hypersurfaces in non-flat complex space forms whose generalized Tanaka-Webster Lie derivative of 1) shape operator, 2) structure Jacobi operator coincides with the covariant derivative of them with respect to any vector field X orthogonal to ${\xi}$ are studied.

• 대한화학회지
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• 제21권5호
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• pp.362-371
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• 1977

이 論文에서는 NMR 吸收線과 FID 曲線의 모양을 硏究함에 있어서의 projection operation의 應用法을 探索하였다. 이 projection operator法은 NMR 吸收線과 FID 函數를 硏究하는데에 基礎가 되는 한 벌의 hierarchy equation들을 誘導하는데에 便利한 手段이 됨을 밝혔다. 逐次近似法이나 적당한 decoupling 近似를 쓰면 이들 方程式은 NMR 吸收線이나 FID 函數를 理論的으로 計算하는데에 좋은 出發點이 될 수 있을 것이다. NMR 吸收線에 對한 간단한 linear response theory의 考察과 吸收線과 FID 函數間의 關係도 記述하였다.

• 호남수학학술지
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• 제26권2호
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• pp.155-161
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• 2004

The shape operator or second fundamental tensor of a real hypersurface in $M_n(c)$ will be denoted by A, and the induced almost contact metric structure of the real hypersurface by (${\phi}$, <, >,${\xi}$, ${\eta}$). The purpose of this paper is to prove that is no ruled real hypersurface M in a complex space form $M_n(c)$, $c{\neq}0$, $n{\geq}3$, who satisfies $R_{\xi}{\phi}={\phi}R_{\xi}$ on M.

• 대한수학회지
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• 제41권3호
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• pp.535-565
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• 2004

In this paper we consider the notion of ξ-invariant or (equation omitted)-invariant real hypersurfaces in a complex two-plane Grassmannian $G_2$( $C^{m+2}$) and prove that there do not exist such kinds of real hypersurfaces in $G_2$( $C^{m+2}$) with parallel second fundamental tensor on a distribution ζ defined by ζ = ξ U(equation omitted), where(equation omitted) = Span ｛ξ$_1$, ξ$_2$, ξ$_3$｝.X>｝.

• 대한수학회지
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• 제44권3호
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• pp.647-659
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• 2007

Relationships between the Ricci curvature and the squared mean curvature and between the shape operator associated with the mean curvature vector and the sectional curvature function for slant submanifolds of an S-space-form are proved, particularizing them to invariant and anti-invariant submanifolds tangent to the structure vector fields.

• 대한수학회논문집
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• 제18권2호
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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 $\varepsilon$.

• 대한수학회논문집
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• 제17권3호
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• pp.519-529
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• 2002

In this paper. We Study (n + 1)-dimensional Contact CR-submanifolds of (n - 1) contact CR-dimension immersed in a Sasakian space form M$\^$2m+1/(c) (2m=n+p, p>0), and especially determine such submanifolds under additional condition concerning with shape operator.