Showing papers by "Jun-ichi Inoguchi published in 2020"

On Magnetic Curves in Almost Cosymplectic Sol Space

Abstract: Magnetic curves with respect to the almost cosymplectic structure of the $$\mathrm {Sol}_3$$ space are determined and curvature properties of these curves are investigated

A characterization of the alpha-connections on the statistical manifold of normal distributions

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.

A Note on Superspirals of Confluent Type

Abstract: Superspirals include a very broad family of monotonic curvature curves, whose radius of curvature is defined by a completely monotonic Gauss hypergeometric function. They are generalizations of log-aesthetic curves, and other curves whose radius of curvature is a particular case of a completely monotonic Gauss hypergeometric function. In this work, we study superspirals of confluent type via similarity geometry. Through a detailed investigation of the similarity curvatures of superspirals of confluent type, we find a new class of planar curves with monotone curvature in terms of Tricomi confluent hypergeometric function. Moreover, the proposed ideas will be our guide to expanding superspirals.

The Gauss maps of Demoulin surfaces with conformal coordinates

Abstract: Demoulin surfaces in real projective $3$-space are investigated. Our result enable 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.