• East Asian mathematical journal
• /
• v.26 no.1
• /
• pp.75-79
• /
• 2010

Let G be a compact connected semisimple Lie group, g the Lie algebra of G, g the canonical metric (the biinvariant Riemannian metric which is induced from the Killing form of g), and $\nabla$ be the Levi-Civita connection for the metric g. Then, we get the fact that the Levi-Civita connection $\nabla$ in the tangent bundle TG over (G, g) is a Yang-Mills connection.

• Bulletin of the Korean Mathematical Society
• /
• v.56 no.6
• /
• pp.1525-1537
• /
• 2019

Let ${\tilde{M}}$ be a Riemannian manifold equipped with a concircular vector field ${\tilde{X}}$ and M a submanifold (with its induced metric) of ${\tilde{M}}$. Denote by X the restriction of ${\tilde{X}}$ on M and by $X^T$ the tangential component of X, called the canonical field of M. In this article we study submanifolds of ${\tilde{M}}$ whose canonical field $X^T$ is also concircular. Several characterizations and classification results in this respect are obtained.

• Journal of the Chungcheong Mathematical Society
• /
• v.23 no.4
• /
• pp.813-821
• /
• 2010

Let G and H be compact connected Lie groups with biinvariant Riemannian metrics g and h respectively, ${\phi}$ a group isomorphism of G onto H, and $E:={\phi}^{-1}TH$ the induced bundle by $\phi$ over the base manifold G of the tangent bundle TH of H. Let ${\nabla}$ and $^H{\nabla}$ be the Levi-Civita connections for the metrics g and h respectively, $\tilde{\nabla}$ the induced connection by the map ${\phi}$ and $^H{\nabla}$. Then, a necessary and sufficient condition for $\tilde{\nabla}$ in the bundle (${\phi}^{-1}TH$, G, ${\pi}$) to be a Yang- Mills connection is the fact that the Levi-Civita connection ${\nabla}$ in the tangent bundle over (G, g) is a Yang- Mills connection. As an application, we get the following: Let ${\psi}$ be an automorphism of a compact connected semisimple Lie group G with the canonical metric g (the metric which is induced by the Killing form of the Lie algebra of G), ${\nabla}$ the Levi-Civita connection for g. Then, the induced connection $\tilde{\nabla}$, by ${\psi}$ and ${\nabla}$, is a Yang-Mills connection in the bundle (${\phi}^{-1}TH$, G, ${\pi}$) over the base manifold (G, g).

• Korean Journal of Mathematics
• /
• v.32 no.3
• /
• pp.467-484
• /
• 2024

In this paper, following the pullback approach to global Finsler geometry, we investigate a coordinate-free study of Shen square metric in a more general manner. Precisely, for a Finsler metric (M, L) admitting a concurrent π-vector field, we study some geometric objects associated with ${\widetilde{L}}(x, y)={\frac{(L+{\mathfrak{B}}^2)}L}$ in terms of the objects of L, where ${\mathfrak{B}}$ is the associated 1-form. For example, we find the geodesic spray, Barthel connection and Berwald connection of ${\widetilde{L}}(x,y)$. Moreover, we calculate the curvature of the Barthel connection of ${\tilde{L}}$. We characterize the non-degeneracy of the metric tensor of ${\widetilde{L}}(x,y)$.

• Communications of the Korean Mathematical Society
• /
• v.35 no.4
• /
• pp.1269-1281
• /
• 2020

In this article, we show that a pseudo-Hermitian magnetic curve in a normal almost contact metric 3-manifold equipped with the canonical affine connection ${\hat{\nabla}}^t$ is a slant helix with pseudo-Hermitian curvature ${\hat{\kappa}}={\mid}q{\mid}\;sin\;{\theta}$ and pseudo-Hermitian torsion ${\hat{\tau}}=q\;cos\;{\theta}$. Moreover, we prove that every pseudo-Hermitian magnetic curve in normal almost contact metric 3-manifolds except quasi-Sasakian 3-manifolds is a slant helix as a Riemannian geometric sense. On the other hand we will show that a pseudo-Hermitian magnetic curve γ in a quasi-Sasakian 3-manifold M is a slant curve with curvature κ = |(t - α) cos θ + q| sin θ and torsion τ = α + {(t - α) cos θ + q} cos θ. These curves are not helices, in general. Note that if the ambient space M is an α-Sasakian 3-manifold, then γ is a slant helix.

• Communications of the Korean Mathematical Society
• /
• v.9 no.2
• /
• pp.393-400
• /
• 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)

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.7 no.4
• /
• pp.819-833
• /
• 2013

Computing global features based on local features using a bio-inspired framework has shown promising performance. However, for some tough applications with large intra-class variances, a single local feature is inadequate to represent all the attributes of the images. To integrate the complementary abilities of multiple local features, in this paper we have extended the efficacy of the bio-inspired framework, HMAX, to adapt heterogeneous features for global feature extraction. Given multiple global features, we propose an approach, designated as parameterized metric learning, for high dimensional feature fusion. The fusion parameters are solved by maximizing the canonical correlation with respect to the parameters. Experimental results show that our method achieves significant improvements over the benchmark bio-inspired framework, HMAX, and other related methods on the Caltech dataset, under varying numbers of training samples and feature elements.

• Journal of the Korean Mathematical Society
• /
• v.41 no.2
• /
• pp.369-378
• /
• 2004

A canonical Finsler connection Nr is defined by a generalized Finsler structure called a (G, N)-structure, where G is a generalized Finsler metric and N is a nonlinear connection given in a differentiable manifold, respectively. If NT is linear, then the(G, N)-structure has a linearity in a sense and is called Berwaldian. In the present paper, we discuss what it means that NT is with a vanishing hv-torsion: ${P^{i}}\;_{jk}\;=\;0$ and introduce the notion of a stronger type for linearity of a (G, N)-structure. For important examples, we finally investigate the cases of a Finsler manifold and a Rizza manifold.

• Journal of the Korean Mathematical Society
• /
• v.41 no.1
• /
• pp.107-130
• /
• 2004

A $JB^{*}-triple$ is a Banach space A on which the group Aut(B) of biholomorphic automorphisms acts transitively on the open unit ball B of A. In this case, a triple product {$\cdots$} from $A\;\times\;A\;\times\;A\;to\;A$ can be defined in a canonical way. If A is also the dual of some Banach space $A_{*}$, then A is said to be a JBW triple. A projection R on A is said to be structural if the identity {Ra, b, Rc} = R{a, Rb, c, }holds. On $JBW^{*}-triples$, structural projections being algebraic objects by definition have also some interesting metric properties, and it is possible to give a full characterization of structural projections in terms of the norm of the predual $A_{*}$ of A. It is shown, that the class of structural projections on A coincides with the class of the adjoints of neutral GL-projections on $A_{*}$. Furthermore, the class of GL-projections on $A_{*}$ is naturally ordered and is completely ortho-additive with respect to L-orthogonality.

• Korean Journal of Ichthyology
• /
• v.34 no.2
• /
• pp.102-112
• /
• 2022

This study investigated dietary habits and intra- and inter-specific food resource partitioning of co-occurring walleye pollock (Gadus chalcogrammus) and Pacific cod (G. macrocephalus) from the waters off the north-eastern coast of South Korea using stomach contents and stable isotopes (δ¹³C and δ¹⁵N) analyses. Both species are mesopelagic carnivores that consumed mainly benthopelagic crustaceans, but teleosts were also abundant in the diet of Pacific cod. Non-metric multidimensional scaling (nMDS) ordination and permutational multivariate analysis of variance (PERMANOVA) of dietary data revealed significant intra- and inter-specific dietary differences, i.e., food resource partitioning. Nitrogen stable isotope values (δ¹⁵N) were similar between walleye pollock and Pacific cod, but carbon stable isotope values (δ¹³C) were significant different, suggesting different trophic positioning. Canonical analysis of principal coordinate (CAP) ordination plot further demonstrated that differences in the type and range of prey ingested by the two species contributed such an inter-specific difference in the diet compositions. Ontogenetic changes in diet compositions were evident. As walleye pollock, they preyed more upon carid shrimps and cephalopods, but no such trend was observed in the diets of Pacific cod. While stable isotope values indicated that large-sized specimens of both species were significantly enriched in ¹⁵N relative to smaller conspecifics thus supporting these data. Consequently, in this study, both methodologies, i.e., stomach contents and stable isotope analyses, provided evidence of inter- and/or intra-specific dietary segregations and trophic niche partitioning between co-occurring walleye pollock and Pacific cod off eastern Korean waters.