Jun-ichi Inoguchi’s research while affiliated with Hokkaido University and other places

... and the first two equations in (20). Similarly, we have identities g ij (e 1 (t), e 2 (t), p 1 (t), p 2 (t)) ≡ 0 that imply the equations ...

Reference:

Contact magnetic geodesic and sub-Riemannian flows on $V_{n,2}$ and integrable cases of a heavy rigid body with a gyrostat

... In our previous work [21] we improved and generalized Theorem 1.2-(ii) of [6]. More precisely, we proved the following theorem. ...

Reference:

Homogeneous structures of $3$-dimensional Lie groups

... Non trivial homogeneous Riemannian structures of type T 2 can exist only on SL 2 R and SE(1, 1). For more detail, see [12,15,27]. ...

Reference:

Homogeneous structures of $3$-dimensional Lie groups

... In this section, we exhibit these Lie groups in detail. For more information on these examples, we refer to [6,7]. ...

Reference:

On Ricci Recurrent Almost Kenmotsu $3$-manifolds

... Recently, submanifold geometry of non-Hermitian symmetric model spaces has been developed. For instance, De Leo and Van der Veken proved the non-existence of totally geodesic hypersurfaces in the model space F 4 [11] (for further details on F 4 , see also [17]). Some minimal submanifolds in the model spaces Sol 4 0 and Sol 4 1 are investigated in [15] and [16,23], respectively. ...

Reference:

Codazzi and totally umbilical hypersurfaces in $\mathrm {Sol}_1^4

... In several cases, no totally umbilical surfaces occur. In the recent paper [6], parallel and totally geodesic hypersurfaces were classified in the four-dimensional Thurston geometry general description for the Gauss map of a nondegenerate (i.e., spacelike or timelike) submanifold in a Lorentzian ambient space. In particular, we shall prove that the Gauss map of a nondegenerate surface in a three-dimensional Lorentzian manifold is conformal if and only if the surface is either totally umbilical or minimal. ...

Reference:

On totally umbilical and minimal surfaces of the Lorentzian Heisenberg groups

... The reductive decomposition corresponding to the naturally reductive homogeneous structure of the Berger 3-sphere and SL 2 R are explicitly given in [31] and [32], respectively. ...

Reference:

Homogeneous structures of $3$-dimensional Sasakian space forms

... In [6], Inoguchi proved that an almost Kenmotsu 3-manifold is locally symmetric if and only if it is isometric to either the hyperbolic space H 3 (−1) or the product space H 2 (−4 − γ 2 ) × R for some γ. This classification result was announced in [2]. ...

Reference:

On Ricci Recurrent Almost Kenmotsu $3$-manifolds

... where ρ is the curvature radius, s is the arc length and α ∈ R is the slope of the linear LCG. The LAC has been discussed in the framework of similarity geometry in [11,12,13], where it is the shape invariant curve with respect to integrable deformation in similarity geometry. It is also shown that the LAC admits the variational formulation in terms of the fairing energy functional. ...

Reference:

A new class of aesthetic curves based on the self-affinity in equiaffine geometry

... The purpose of this paper is to study conformal trajectories in the space forms R 3 , S 3 and H 3 . For magnetic fields, the study of magnetic trajectories in space forms have been developed in [3,4,5,8,9,10,12]. In each of these space forms, we will consider particular examples of proper conformal vector fields. ...

Reference:

Conformal trajectories in 3-dimensional space form