• Bulletin of the Korean Mathematical Society
• /
• v.40 no.2
• /
• pp.327-340
• /
• 2003

We are devoted to dealing with the conformal theory of a Rizza manifold with a generalized Finsler metric $G_{ij}$ (x,y) and a new conformal invariant non-linear connection $M^{i}$ $_{j}$ (x,y) constructed from the generalized Cern's non-linear connection $N^{i}$ $_{j}$ (x,y) and almost complex structure $f^{i}$ $_{j}$ (x). First, we find a conformal invariant connection ( $M_{j}$ $^{i}$ $_{k}$ , $M^{i}$ $_{j}$ , $C_{j}$ $^{i}$ $_{k}$ ) and conformal invariant tensors. Next, the nearly Kaehlerian (G, M)-structures under conformal change in a Rizza manifold are investigate.

• Bulletin of the Korean Mathematical Society
• /
• v.40 no.1
• /
• pp.85-89
• /
• 2003

Let V be a localizing infinite-dimensional complex Banach space. Let X be a flag manifold of finite flags either of finite codimensional closed linear subspaces of V or of finite dimensional linear subspaces of V. Let E be a holomorphic vector bundle on X with finite rank. Here we prove that E is uniform, i.e. that for any two lines $D_1$ R in the same system of lines on X the vector bundles E$\mid$D and E$\mid$R have the same splitting type.

• Communications of the Korean Mathematical Society
• /
• v.17 no.3
• /
• pp.505-517
• /
• 2002

We introduce certain conformally invariant h-Finsler connection in a Rizza manifold. Using this connection, we find some conformally invariant Finsler tensors. The conformal flatness and the Kaehlerian Finsler manifold with respect to the above connection are investigated.

• Communications of the Korean Mathematical Society
• /
• v.29 no.1
• /
• pp.141-153
• /
• 2014

In this article, we apply the weak maximum principle in order to obtain a suitable characterization of the complete linearWeingarten hypersurfaces immersed in locally symmetric Riemannian manifold $N^{n+1}$. Under the assumption that the mean curvature attains its maximum and supposing an appropriated restriction on the norm of the traceless part of the second fundamental form, we prove that such a hypersurface must be either totally umbilical or hypersurface is an isoparametric hypersurface with two distinct principal curvatures one of which is simple.

• Journal of KIISE:Software and Applications
• /
• v.31 no.2
• /
• pp.182-188
• /
• 2004

This paper proposes to synthesize facial images from a few parameters for the pose and the expression of their constituent components. This parameterization makes the representation, storage, and transmission of face images effective. But it is difficult to parameterize facial images because variations of face images show a complicated nonlinear manifold in high-dimensional data space. To tackle this problem, we use an LLE (Locally Linear Embedding) technique for a good representation of face images, where the relationship among face images is preserving well and the projected manifold into the reduced feature space becomes smoother and more continuous. Next, we apply a snake model to estimate face feature values in the reduced feature space that corresponds to a specific pose and/or expression parameter. Finally, a synthetic face image is obtained from an interpolation of several neighboring face images in the vicinity of the estimated feature value. Experimental results show that the proposed method shows a negligible overlapping effect and creates an accurate and consistent synthetic face images with respect to changes of pose and/or expression parameters.

• 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.

• 제어로봇시스템학회:학술대회논문집
• /
• 1994.10a
• /
• pp.628-633
• /
• 1994

A new Riemannian geometric model for the controlled plant is proposed by imbedding the control vector space in the state space, so as to reduce the dimension of the model. This geometric model is derived by replacing the orthogonal straight coordinate axes on the state space of a linear system with the curvilinear coordinate axes. Therefore the integral manifold of the geometric model becomes homeomorphic to that of fictitious linear system. For the lower dimensional Riemannian geometric model, a nonlinear optimal regulator with a quadratic form performance index which contains the Riemannian metric tensor is designed. Since the integral manifold of the nonlinear regulator is determined to be homeomorphic to that of the linear regulator, it is expected that the basic properties of the linear regulator such as feedback structure, stability and robustness are to be reflected in those of the nonlinear regulator. To apply the above regulator theory to a real nonlinear plant, it is discussed how to distort the curvilinear coordinate axes on which a nonlinear plant behaves as a linear system. Consequently, a partial differential equation with respect to the homeomorphism is derived. Finally, the computational algorithm for the nonlinear optimal regulator is discussed and a numerical example is shown.

• Proceedings of the IEEK Conference
• /
• 2008.06a
• /
• pp.979-980
• /
• 2008

In this paper we use the Isometric Projection, a linear subspace method, for manifold representation of the pose-varying-faces. Isometric Projection method for pose identification is evaluated on view varying faces and is compared with other global and local linear subspace methods.

• Journal of the Chungcheong Mathematical Society
• /
• v.36 no.3
• /
• pp.163-169
• /
• 2023

In this article, we consider a vectorial linear connection which is determined by three fixed vector fields. Classifying these vectorial connections, we obtain a new type of generalized statistical manifolds which allow non-zero torsion.

• Communications of the Korean Mathematical Society
• /
• v.38 no.2
• /
• pp.621-628
• /
• 2023

Given a linear connection ∇ and its dual connection ∇^*, we discuss the situation where ∇ + ∇^* = 0. We also discuss statistical manifolds with torsion and give new examples of some type for linear connections inducing the statistical manifolds with non-zero torsion.