Showing papers by "Jun-ichi Inoguchi published in 2007"

Biharmonic curves in 3-dimensional Sasakian space forms

Abstract: We show that every proper biharmonic curve in a 3-dimensional Sasakian space form of constant holomorphic sectional curvature H is a helix (both of whose geodesic curvature and geodesic torsion are constants). In particular, if H ≠ 1, then it is a slant helix, that is, a helix which makes constant angle α with the Reeb vector field with the property \(\kappa^{2}+\tau^{2}=1+(H-1)\sin^{2}\alpha\). Moreover, we construct parametric equations of proper biharmonic herices in Bianchi–Cartan–Vranceanu model spaces of a Sasakian space form.

Parallel surfaces in the motion groups E(1,1) and E(2),

Abstract: We give a classification of parallel surfaces in the groups of rigid motions of Minkowski plane and Euclidean plane, equipped with a general left-invariant metric Our result completes the classification of parallel surfaces in the eight three-dimensional model geometries of Thurston and in three-dimensional unimodular Lie groups with maximal isometry group

Helicoids and axially symmetric minimal surfaces in 3-dimensional homogeneous spaces

Abstract: The Bianchi-Cartan-Vranceanu spaces are Riemannian 3-manifolds whose isometry groups have at least 4-dimension and not of constant neg- ative curvature. In this paper we study helicoids and axially symmetric minimal surfaces in the Bianchi-Cartan-Vranceanu spaces. In particular, axially symmetric minimal surfaces are explicitly classifled in terms of el- liptic functions. Moreover the non-existence of totally umbilical surfaces in the irreducible Bianchi-Cartan-Vranceanu spaces is proved.

Deformations of Surfaces Preserving Conformal or Similarity Invariants

Abstract: We study Mobius applicable surfaces, i.e., conformally immersed surfaces in Mobius 3-space which admit deformations preserving the Mobius metric. We show new characterizations of Willmore surfaces, Bonnet surfaces and harmonic inverse mean curvature surfaces in terms of Mobius or similarity invariants.