• 충청수학회지
• /
• 제24권4호
• /
• pp.825-832
• /
• 2011

In this paper, we make a minute and detailed proof of a part which is omitted in the process of obtaining the value of the curvature tensor for an invariant affine connection at the point {H} of a reductive homogeneous space G/H in the paper 'Invariant affine connections on homogeneous spaces' by K. Nomizu.

• 대한수학회보
• /
• 제33권3호
• /
• pp.455-463
• /
• 1996

In [3] and [4], Kitahara, Pak and the author obtained the conformally invariant tensor $B_0$, which is an algebraic Hermitian analogue of the Weyl conformal curvature tensor W in the Riemannian geometry, by the decomposition of the curvature tensor H of the Hermitian connection and the notion of semi-curvature-like tensors of Tanno (see[7]). In [5], the author defined a conformally invariant tensor $B_0$ on a Hermitian manifold as a modification of $B_0$. Moreover he introduced the notion of local conformal Hermitian-flatness of Hermitian manifolds and proved that the vanishing of this tensor $B_0$ together with some condition for the scalar curvatures is a necessary and sufficient condition for a Hermitian manifold to be locally conformally Hermitian-flat.

• 충청수학회지
• /
• 제28권2호
• /
• pp.229-241
• /
• 2015

In this paper, we decompose the curvature tensor (field) on the homogeneous Riemannian manifold SU(3)=T (k, l) with an arbitrarily given SU(3)-invariant Riemannian metric into three curvature-like tensor fields, and investigate geometric properties.

• 대한수학회보
• /
• 제42권1호
• /
• pp.93-119
• /
• 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 $\xi$.

• 대한수학회보
• /
• 제46권2호
• /
• pp.289-294
• /
• 2009

We show that on a Hermitian surface M, if M is weakly *-Einstein and has J-invariant Ricci tensor then M is Einstein, and vice versa. As a consequence, we obtain that a compact *-Einstein Hermitian surface with J-invariant Ricci tensor is $K{\ddot{a}}hler$. In contrast with the 4- dimensional case, we show that there exists a compact Einstein Hermitian (4n + 2)-dimensional manifold which is not weakly *-Einstein.

• 자원환경지질
• /
• 제52권1호
• /
• pp.81-90
• /
• 2019

본 연구는 이차원 DFN(discrete fracture network) 시스템에서 절리의 빈도 및 길이분포에 따른 절리텐서의 성분 및 일차불변량이 DFN의 블록수리전도 특성에 미치는 영향을 평가하였다. 확정적인 두 방향의 절리군을 사용하여 절리군의 빈도와 길이분포에 따라 생성된 총 36개의 DFN 시스템에서 각각 매 $30^{\circ}$ 간격으로 설정된 수두경사에 따른 블록수리전도도와 절리텐서의 성분 간의 상관성 분석이 수행되었다. DFN 블록의 블록수리전도도는 이에 직교하는 방향의 절리텐서 성분과 강한 상관관계를 갖는다. 본 연구의 연결성을 유지한 DFN 시스템은 절리텐서의 일차불변량이 2.0~2.5 이상일 때 등가의 연속체 해석이 가능한 것으로 평가되었다. 절리텐서의 일차불변량은 평균 블록수리전도도와 매우 강한 함수관계를 갖으며 DFN 시스템의 블록수리전도 특성을 평가하는 데에 사용될 수 있다. 또한, 본 연구를 통하여 절리텐서의 일차불변량을 이용한 DFN 시스템의 업스케일링 가능성이 논의되었다.

• 대한기계학회논문집
• /
• 제18권4호
• /
• pp.967-976
• /
• 1994

A tensor invariant model equation for the turbulent energy dissipation rate is proposed in the present study, which is able to simulate secondary straining effects such as curvature effects without the introduction of additional empirical input. The source term in this model has a combined form of the generation term due to the mean vorticity with the conventional one due to the mean strain rate. An extended low-Reynolds-number $k-\epsilon$ turbulence model involving this new model equation is tested for a turbulent Coutte flow between coaxial cylinders with inner cylinder rotated, which is a well defined example of curved flows. The predicted results indicate that the present model works much better for this flow, compared with previous models.

• 대한기계학회논문집
• /
• 제18권1호
• /
• pp.184-192
• /
• 1994

The parameters such as Richardson numbers or stability parameters are widely used to account for the extra straining effects due to three-dimensionality, curvature, rotation, swirl and others arising in paractical complex flows. Existing expressions for the extra strain in turbulence models such as $k-{\epsilon}$ models, however, do not satisfy the tensor invariant condition representing the coordinate indifference. In the present paper, considering the characteristics of both the mean strain rate and the mean vorticity, a new parameter to deal with the extra straining effects is proposed. The new parameter has a simple form and satisfies the tensor invariant condition. A semi-quantitative analysis between the present and previous parameters for several typical complex flows suggests that the newly proposed parameter is more general and adequate in representing the extra straining effects than the previous ad-hoc parameters.

• Kyungpook Mathematical Journal
• /
• 제61권1호
• /
• pp.191-203
• /
• 2021

Let M be an almost Kenmotsu manifold of dimension 2n + 1 having non-vanishing ��-sectional curvature such that trℓ > -2n - 2. We prove that any second order parallel tensor on M is a constant multiple of the associated metric tensor and obtained some consequences of this. Vector fields keeping curvature tensor invariant are characterized on M.

• East Asian mathematical journal
• /
• 제38권5호
• /
• 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.