Showing papers by "Jun-ichi Inoguchi published in 2009"
TL;DR: The notion of biharmonic map between Riemannian manifolds was generalized to maps from RiemANNIAN manifolds into affine manifolds in this article, where Hopf cylinders in 3-dimensional Sasakian space forms which are bi-harmonic with respect to Tanaka-Webster connection were classified.
Abstract: The notion of biharmonic map between Riemannian manifolds is generalized to maps from Riemannian manifolds into affine manifolds. Hopf cylinders in 3-dimensional Sasakian space forms which are biharmonic with respect to Tanaka-Webster connection are classified.
14 citations
TL;DR: In this paper, the authors show that all Sasakian 3-manifolds are pseudo-symmetric spaces of constant type, and that they are homogeneous 3-menifolds.
Abstract: Contact Homogeneous 3-manifolds are pseudo-symmetric spaces of constant type. All Sasakian 3-manifolds are pseudo-symmetric spaces of constant type.
13 citations
Posted Content•
TL;DR: Biharmonic or polyharmonic curves and surfaces in 3-dimensional contact manifolds are investigated in this article, where the authors consider the case where the surfaces are polyharmonically connected.
Abstract: Biharmonic or polyharmonic curves and surfaces in 3-dimensional contact manifolds are investigated.
10 citations
DOI•
08 Apr 2009
TL;DR: In this paper, it was shown that the tangent sphere bundles over surfaces are pseudo-symmetric if and only if the base surfaces are of constant curvature, and that the semi symmetry depends on the radius of the base surface.
Abstract: The tangent sphere bundles over surfaces are pseudo-symmetric if and only if the base surfaces are of constant curvature. It is pointed out that semi-symmetry of the tangent sphere bundle of a surface of constant positive curvature depends on the radius.
8 citations
Posted Content•
TL;DR: In this article, all biharmonic homogeneous real hypersurfaces in the complex or quaternionic projective spaces are classified in case of bounded geometry to Chen's conjecture or Caddeo, Montaldo and Piu's one.
Abstract: Classifications of all biharmonic isoparametric hypersurfaces in the unit sphere, and all biharmonic homogeneous real hypersurfaces in the complex or quaternionic projective spaces are shown. Answers in case of bounded geometry to Chen's conjecture or Caddeo, Montaldo and Piu's one on biharmonic maps into a manifold of non positive curvature are given. Gauge field analogue is shown, and the isolation phenomena of bi-Yang-Mills fields are obtained.
6 citations
6 citations
Posted Content•
TL;DR: In this article, constant mean curvature surfaces with vertically harmonic Gau{\ss} map with canonical Riemannian and Lorentzian metrics are classified. But they do not consider the case of continuous curvatures.
Abstract: Invariant minimal surfaces in the real special linear group of degree 2 with canonical Riemannian and Lorentzian metrics are studied. Constant mean curvature surfaces with vertically harmonic Gau{\ss} map are classified.
5 citations
TL;DR: In this paper, the Grassmann geometry of surfaces when the ambient space is a 3-dimensional unimodular Lie group with left invariant metric was studied, and the Grassman geometry was extended to the case of surfaces.
Abstract: We study the Grassmann geometry of surfaces when the ambient space is a 3-dimensional unimodular Lie group with left invariant metric, that is, it is one of the 3-dimensional commutative Lie group, the 3-dimensional Heisenberg group, the groups of rigid motions on the Euclidean or the Minkowski planes, the special unitary group $SU(2)$, and the special real linear group $SL(2,\mathbb R)$.
4 citations