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Jun-ichi Inoguchi

Bio: Jun-ichi Inoguchi is an academic researcher from University of Tsukuba. The author has contributed to research in topics: Curvature & Mean curvature. The author has an hindex of 22, co-authored 123 publications receiving 1580 citations. Previous affiliations of Jun-ichi Inoguchi include Yamagata University & Utsunomiya University.


Papers
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Journal ArticleDOI
TL;DR: In this article, the authors investigated periodic magnetic curves in elliptic Sasakian space forms and obtained a quantization principle for periodic magnetic flowlines on Berger spheres, and gave a criterion for periodicity of magnetic curves on the unit sphere.
Abstract: It is an interesting question whether a given equation of motion has a periodic solution or not, and in the positive case to describe it. We investigate periodic magnetic curves in elliptic Sasakian space forms and we obtain a quantization principle for periodic magnetic flowlines on Berger spheres. We give a criterion for periodicity of magnetic curves on the unit sphere ${\mathbb{S}}^3$.

27 citations

Journal ArticleDOI
TL;DR: In this article, the authors construct explicit solutions to discrete motion of discrete plane curves, which has been introduced by one of the authors recently, and present explicit formulas in terms of the function.
Abstract: We construct explicit solutions to discrete motion of discrete plane curves which has been introduced by one of the authors recently. Explicit formulas in terms the function are presented. Transformation theory of motions of both smooth and discrete curves is developed simultaneously.

27 citations

Journal ArticleDOI
TL;DR: In this paper, the classification of surfaces with parallel second fundamental form in all three-dimensional homogeneous spaces is complete, i.e., surfaces with the same fundamental form on all three dimensions.
Abstract: We complete the classification of surfaces with parallel second fundamental form in all three-dimensional homogeneous spaces.

25 citations

Journal ArticleDOI
TL;DR: In this article, a classification of parallel surfaces in the groups of rigid motions of Minkowski plane and Euclidean plane equipped with a general left-invariant metric was given.
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

24 citations

Journal ArticleDOI
TL;DR: In this article, the authors give loop group theoretic reformulated Backlund transformations on constant mean curvature timelike surfaces in Minkowski 3-space and present 1-soliton surfaces explicitly.

22 citations


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Book
08 Dec 2004
TL;DR: In this article, the Darboux transformation is applied to the 2-dimensional Gelfand-Dickey system and the result is that the transformation is invariant to the dimension of the system.
Abstract: Preface.- 1. 1+1 Dimensional Integrable Systems.- 1.1 KdV equation, MKdV equation and their Darboux transformations. 1.1.1 Original Darboux transformation. 1.1.2 Darboux transformation for KdV equation. 1.1.3 Darboux transformation for MKdV equation. 1.1.4 Examples: single and double soliton solutions. 1.1.5 Relation between Darboux transformations for KdV equation and MKdV equation. 1.2 AKNS system. 1.2.1 2 x 2 AKNS system. 1.2.2 N x N AKNS system. 1.3 Darboux transformation. 1.3.1 Darboux transformation for AKNS system. 1.3.2 Invariance of equations under Darboux transformations. 1.3.3 Darboux transformations of higher degree and the theorem of permutability. 1.3.4 More results on the Darboux matrices of degree one. 1.4 KdV hierarchy, MKdV-SG hierarchy, NLS hierarchy and AKNS system with u(N) reduction. 1.4.1 KdV hierarchy. 1.4.2 MKdV-SG hierarchy. 1.4.3 NLS hierarchy. 1.4.4 AKNS system with u(N) reduction. 1.5 Darboux transformation and scattering, inverse scattering theory. 1.5.1 Outline of the scattering and inverse scattering theory for the 2 x 2 AKNS system . 1.5.2 Change of scattering data under Darboux transformations for su(2) AKNS system. 2. 2+1 Dimensional Integrable Systems.- 2.1 KP equation and its Darboux transformation. 2.2 2+1 dimensional AKNS system and DS equation. 2.3 Darboux transformation. 2.3.1 General Lax pair. 2.3.2 Darboux transformation of degree one. 2.3.3 Darboux transformation of higher degree and the theorem of permutability. 2.4 Darboux transformation and binary Darboux transformation for DS equation. 2.4.1 Darboux transformation for DSII equation. 2.4.2 Darboux transformation and binary Darboux transformation for DSI equation. 2.5 Application to 1+1 dimensional Gelfand-Dickey system. 2.6 Nonlinear constraints and Darboux transformation in 2+1 dimensions. 3. N + 1 Dimensional Integrable Systems.- 3.1 n + 1 dimensional AKNS system. 3.1.1 n + 1 dimensional AKNS system. 3.1.2Examples. 3.2 Darboux transformation and soliton solutions. 3.2.1 Darboux transformation. 3.2.2 u(N) case. 3.2.3 Soliton solutions. 3.3 A reduced system on Rn. 4. Surfaces of Constant Curvature, Backlund Congruences.- 4.1 Theory of surfaces in the Euclidean space R3. 4.2 Surfaces of constant negative Gauss curvature, sine-Gordon equation and Backlund transformations. 4.2.1 Relation between sine-Gordon equation and surface of constant negative Gauss curvature in R3. 4.2.2 Pseudo-spherical congruence. 4.2.3 Backlund transformation. 4.2.4 Darboux transformation. 4.2.5 Example. 4.3 Surface of constant Gauss curvature in the Minkowski space R2,1 and pseudo-spherical congruence. 4.3.1 Theory of surfaces in the Minkowski space R2,1. 4.3.2 Chebyshev coordinates for surfaces of constant Gauss curvature. 4.3.3 Pseudo-spherical congruence in R2,1. 4.3.4 Backlund transformation and Darboux transformation for surfaces of constant Gauss curvature in R2,1. 4.4 Orthogonal frame and Lax pair. 4.5 Surface of constant mean curvature. 4.5.1 Parallel surface in Euclidean space. 4.5.2 Construction of surfaces. 4.5.3 The case in Minkowski space. 5. Darboux Transformation and Harmonic Map.- 5.1 Definition of harmonic map and basic equations. 5.2 Harmonic maps from R2 or R1,1 to S2, H2 or S1,1. 5.3 Harmonic maps from R1,1 to U(N). 5.3.1 Riemannian metric on U(N). 5.3.2 Harmonic maps from R1,1 to U(N). 5.3.3 Single soliton solutions. 5.3.4 Multi-soliton solutions. 5.4 Harmonic maps from R2 to U(N). 5.4.1 Harmonic maps from R2 to U(N) and their Darboux transformations. 5.4.2 Soliton solutions. 5.4.3 Uniton. 5.4.4 Darboux transformation and singular Darboux transformation for unitons. 6. Generalized Self-Dual Yang-Mills and Yang-Mills-Higgs Equations.- 6.1 Generalized self-dual Yang-Mills flow. 6.1.1 Generalized self-dual Yang-Mills flow. 6.1.2 Darboux transformation. 6.1.3 Example. 6.1.4 Relation with AKNS system. 6.2 Yang-Mills-Higgs

255 citations

Journal ArticleDOI
01 Jul 1960-Nature
TL;DR: In this paper, the Confluent Hypergeometric Functions (CGF) are used to express the hypergeometric functions of a given hypergeometrical function in the form of a convex polygon.
Abstract: Confluent Hypergeometric Functions By Dr L J Slater Pp ix + 247 (Cambridge: At the University Press, 1960) 65s net

194 citations

Journal Article
TL;DR: In this paper, a natural generalization of harmonic maps and minimal immersions can be given by considering the functionals obtained integrating the square of the norm of the tension field or of the mean curvature vector field, respectively.
Abstract: and the corresponding Euler-Lagrange equation is H = 0, where H is the mean curvature vector field. If φ : (M, g) → (N, h) is a Riemannian immersion, then it is a critical point of the bienergy in C∞(M,N) if and only if it is a minimal immersion [26]. Thus, in order to study minimal immersions one can look at harmonic Riemannian immersions. A natural generalization of harmonic maps and minimal immersions can be given by considering the functionals obtained integrating the square of the norm of the tension field or of the mean curvature vector field, respectively. More precisely: • biharmonic maps are the critical points of the bienergy functional E2 : C∞(M,N) → R, E2(φ) = 12 ∫

178 citations

Journal ArticleDOI
30 Apr 2014
TL;DR: In this article, the authors review part of the classical theory of curves and surfaces in 3D Lorentz-Minkowski space and focus in spacelike surfaces with constant mean curvature pointing the differences and similarities with the Euclidean space.
Abstract: We review part of the classical theory of curves and surfaces in 3-dimensional Lorentz-Minkowski space. We focus in spacelike surfaces with constant mean curvature pointing the differences and similarities with the Euclidean space.

175 citations