Showing papers by "Jun-ichi Inoguchi published in 2023"
TL;DR: In this paper , the authors consider magnetic curves corresponding to the Killing magnetic fields in hyperbolic 3-space and show that these curves correspond to the same magnetic fields as the ones in this paper.
Abstract: We consider magnetic curves corresponding to the Killing magnetic fields in hyperbolic 3-space.
TL;DR: In this paper , it was shown that an almost cosymplectic manifold is semi-symmetric if and only if its fundamental endomorphism field is a harmonic unit vector field.
Abstract: In this paper, we study the semi-symmetry and pseudo-symmetry of almost cosymplectic [Formula: see text]-manifolds. First, we prove that an [Formula: see text]-almost cosymplectic [Formula: see text]-manifold [Formula: see text] is semi-symmetric if and only if it is cosymplectic. Here by an [Formula: see text]-almost cosymplectic [Formula: see text]-manifold, we mean an almost cosymplectic [Formula: see text]-manifold whose characteristic vector field [Formula: see text] is a harmonic unit vector field. If an almost cosymplectic [Formula: see text]-manifold [Formula: see text] whose fundamental endomorphism field [Formula: see text] is parallel in the direction of the characteristic vector field [Formula: see text] ([Formula: see text]), then it is [Formula: see text]-almost cosymplectic. In particular, an almost cosymplectic [Formula: see text]-manifold [Formula: see text] satisfying [Formula: see text] is semi-symmetric if and only if it is cosymplectic. Next, we prove that pseudo-symmetric [Formula: see text]-almost cosymplectic [Formula: see text]-manifolds are certain generalized almost cosymplectic [Formula: see text]-spaces.
24 Mar 2023
TL;DR: In this article , the authors studied hypersurfaces of the four-dimensional Thurston geometry and gave a closed expression for the Riemann curvature tensor of a hypersurface with the second fundamental form a Codazzi tensor.
Abstract: We study hypersurfaces of the four-dimensional Thurston geometry $\text{Sol}^4_0$, which is a Riemannian homogeneous space and a solvable Lie group. In particular, we give a full classification of hypersurfaces whose second fundamental form is a Codazzi tensor, including totally geodesic hypersurfaces and hypersurfaces with parallel second fundamental form, and of totally umbilical hypersurfaces of $\text{Sol}^4_0$. We also give a closed expression for the Riemann curvature tensor of $\text{Sol}^4_0$, using two integrable complex structures.