Showing papers by "Jun-ichi Inoguchi published in 2021"
TL;DR: In this paper, the authors classified the magnetic trajectories corresponding to contact magnetic fields in Sasakian manifolds of arbitrary dimension and proved that the codimension of the magnetic curve may be reduced to 2.
Abstract: In this paper we classify the magnetic trajectories corresponding to contact magnetic fields in Sasakian manifolds of arbitrary dimension. Moreover, when the ambient is a Sasakian space form, we prove that the codimension of the curve may be reduced to 2. This means that the magnetic curve lies on a 3-dimensional Sasakian space form, embedded as a totally geodesic submanifold of the Sasakian space form of dimension (2n+1).
57 citations
TL;DR: Magnetic curves with respect to the canonical contact structure of the space Sol3 are investigated in this article, where the authors show that the magnetic curves of Sol3 can be characterized by the following properties:
Abstract: Magnetic curves with respect to the canonical contact structure of the space Sol3 are investigated.
9 citations
TL;DR: In this paper, the authors proposed a method to control the magnitudes of local maximum curvature in a new scheme called extended- or $$\epsilon \kappa $$¯¯ -curves.
Abstract: The $$\kappa $$
-curve is a recently published interpolating spline which consists of quadratic Bezier segments passing through input points at the loci of local curvature extrema. We extend this representation to control the magnitudes of local maximum curvature in a new scheme called extended- or $$\epsilon \kappa $$
-curves.
$$\kappa $$
-curves have been implemented as the curvature tool in Adobe Illustrator® and Photoshop® and are highly valued by professional designers. However, because of the limited degrees of freedom of quadratic Bezier curves, it provides no control over the curvature distribution. We propose new methods that enable the modification of local curvature at the interpolation points by degree elevation of the Bernstein basis as well as application of generalized trigonometric basis functions. By using $$\epsilon \kappa $$
-curves, designers acquire much more ability to produce a variety of expressions, as illustrated by our examples.
7 citations
01 Jul 2021
TL;DR: In this article, it was shown that the statistical manifold of normal distributions admits a 2-dimensional solvable Lie group structure and a geometric characterization of the Amari-Chentsov connection on the Lie group.
Abstract: We show that the statistical manifold of normal distributions is homogeneous. In particular, it admits a 2-dimensional solvable Lie group structure. In addition, we give a geometric characterization of the Amari–Chentsov
$$\alpha $$
-connections on the Lie group.
3 citations
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TL;DR: In this paper, it was shown that a unit vector field on an oriented Riemannian manifold is a critical point of the Landau Hall functional if and only if it is critical point in the Dirichlet energy functional.
Abstract: We show that a unit vector field on an oriented Riemannian manifold is a critical point of the Landau Hall functional if and only if it is a critical point of the Dirichlet energy functional. Therefore, we provide a characterization for a unit vector field to be a magnetic map into its unit tangent sphere bundle. Then, we classify all magnetic left invariant unit vector fields on $3$-dimensional Lie groups.
TL;DR: In this paper, a generalized Weierstrass type representation for definite Demoulin surfaces was established by virtue of primitive maps into a certain semi-Riemannian 6-symmetric space.
Abstract: Demoulin surfaces in the real projective 3-space are investigated. Our result enables us to establish a generalized Weierstrass type representation for definite Demoulin surfaces by virtue of primitive maps into a certain semi-Riemannian 6-symmetric space.