Journal ArticleDOI
Affine Biharmonic Curves in 3-Dimensional Homogeneous Geometries
Jun-ichi Inoguchi,Ji Eun Lee +1 more
TLDR
In this paper, the authors studied affine biharmonic curves in model spaces of Thurston geometry except Sol and showed that every 3-dimensional Riemannian manifold with 4-dimensional isometry group admits a normal almost contact structure compatible to the metric.Abstract:
Every 3-dimensional Riemannian manifold with 4-dimensional isometry group admits a normal almost contact structure compatible to the metric. In this paper we study affine biharmonic curves in model spaces of Thurston geometry except Sol.read more
Citations
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Journal ArticleDOI
Three-dimensional geometry and topology. Volume 1, by William P. Thurston, (edited by Sylvio Levy). Princeton Mathematical Series, 35. £29.95. 1997. ISBN 0-691-08304-5 (Princeton University Press).
Journal ArticleDOI
Magnetic curves in quasi-Sasakian 3-manifolds
TL;DR: In this paper, the authors studied magnetic trajectories corresponding to contact magnetic fields in 3-dimensional quasi-Sasakian manifolds and proved that such magnetic curves are geodesics for a certain linear connection for which all four structure tensor fields are parallel.
Journal ArticleDOI
Slant curves in 3-dimensional almost contact metric geometry
Jun-ichi Inoguchi,Ji Eun Lee +1 more
TL;DR: A survey on slant curves in 3D almost contact metric geometry can be found in this paper, where a 3D solvable Lie group equipped with a natural left invariant almost contact structure is considered.
Journal ArticleDOI
On slant curves in normal almost contact metric 3-manifolds
Jun-ichi Inoguchi,Ji-Eun Lee +1 more
TL;DR: In this article, the authors studied slant curves in almost contact metric 3-manifolds equipped with canonical connection and showed that the mean curvature is proper with respect to the canonical connection.
Journal ArticleDOI
Biharmonic curves into quadrics
Stefano Montaldo,Andrea Ratto +1 more
TL;DR: In this paper, an algebraic method to study biharmonic curves into an implicit surface was developed, which is especially suitable to study curves in surfaces defined by a polynomial equation.
References
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Book
Riemannian Geometry of Contact and Symplectic Manifolds
TL;DR: In this article, the authors describe a complex geometry model of Symplectic Manifolds with principal S1-bundles and Tangent Sphere Bundles, as well as a negative Xi-sectional Curvature.
MonographDOI
Selected Topics in Harmonic Maps
James Eells,Luc Lemaire +1 more
TL;DR: In this article, the authors present a bibliography for differential geometric aspects of harmonic maps and problems relating to harmonic maps, as well as a supplementary bibliography with more details.
Journal ArticleDOI
Another Report on Harmonic Maps
James Eells,Luc Lemaire +1 more
TL;DR: In this paper, it was shown that a map (f>:{M,g)-+(N,h) between Riemannian manifolds which is continuous and of class L\\ is harmonic if and only if it is a critical point of the energy functional.