数学-Mathematics-
論文-Papers-
[64] (with N. Nakatsuyama)
On vertices of frontals in the Euclidean plane.
Bulletin of the Brazilian Mathematical Society, New Series. Vol. 55, 35 (2024) DOI: 10.1007/s00574-024-00410-x
[63]
On geodesics of framed surfaces in the Euclidean 3-space.
Tohoku Mathematical Journal.Vol. 76 (2024) 199--215. DOI: 10.2748/tmj.20221020
[62] (with H. Yu)
On generalised framed surfaces in the Euclidean space.
AIMS Mathematics. Vol. 9 (7), (2024) 17716--17742. DOI: 10.3934/math.2024861
[61] (with L. Chen)
Lightcone framed curves in the Lorentz-Minkowski 3-space.
Turkish Journal of Mathematics. Vol. 48, no. 2 (2024) 307--326. DOI: 10.55730/1300-0098.3508
[60] (with L. Chen, S. Izumiya)
Duality and geometry of horocyclic evolutes in hyperbolic plane.
Research in the Mathematical Sciences. Vol. 11, no. 17 (2024) DOI.10.1007/s40687-024-00434-1
[59] (with S. Honda, H. Yu)
Bertrand and Mannheim curves of framed curves in the 4-dimensional Euclidean space.
Journal of Geometry. Vol. 114, 12 (2023) DOI. 10.1007/s00022-023-00673-7
[58] (with Y. Kabata)
One-parameter families of Legendre curves and plane line congruences.
Mathematische Nachrichten. Vol. 295, no. 8 (2022) 1533--1561. DOI: 10.1002/mana.201900327
[57] (with E. Li, D. Pei)
Enveloids of Legendre curves in the unit tangent bundle over the Euclidean plane.
Bulletin of the Malaysian Mathematical Sciences Society. Vol. 45, no. 6 (2022) 3011--3041. DOI: 10.1007/s40840-022-01320-1
[56] (with H. Yu)
Bertrand and Mannheim curves of spherical framed curves in a three-dimensional sphere.
Mathematics. Vol. 10, no. 8, 1292 (2022) DOI: 10.3390/math10081292
[55] (with T. Fukunaga)
Singularities of translation surfaces of framed curves in the Euclidean 3-space.
Results in Mathematics. Vol. 77, no. 2, Paper No. 89 (2022) DOI: 10.1007/s00025-022-01622-7
[54]
Equi-affine plane curves with singular points.
Journal of Geometry. Vol. 113, no. 1, Paper No. 16 (2022) DOI: 10.1007/s00022-022-00632-8
[53] (with K. Saji)
Singularities of singular solutions of first order differential equations of Clairaut type.
Journal of Dynamical and Control Systems. Vol. 28 (2022), 19--41. DOI: 10.1007/s10883-020-09511-4
[52] (with H. Yu)
Envelopes of families of framed surfaces and singular solutions of first order partial differential equations.
Proceedings of the Royal Society of Edinburgh Section A: Mathematics. Vol. 151 (2021), 1515-1542. DOI: 10.1017/prm.2020.71
[51] (with S. Izumiya, M. C. Romero-Fuster, K. Saji)
Horo-flat surfaces along cuspidal edges in the hyperbolic space.
Journal of Singulariteis. Vol. 22 (2020), 40--58. DOI: 10.5427/jsing.2020.22d
[50] (with S. Honda)
Bertrand and Mannheim curves of framed curves in the 3-dimensional Euclidean space.
Turkish Journal of Mathematics. Vol. 44 (2020), 883--899. DOI: 10.3906/mat-1905-63
[49] (with L. Chen, D. Pei)
Dualities and envelopes of one-parameter families of frontals in hyperbolic and de Sitter 2-space.
Mathematische Nachrichten. Vol. 293 (2020), 893--909. DOI: 10.1002/mana.201800316
[48] (with S. Izumiya)
On families of Lagrangian submanifolds.
Journal of Singularities. Vol. 21 (2020), 188--207. DOI: 10.5427/jsing.2020.21j
[47] (with T. Fukunaga)
Framed surfaces and one-parameter families of framed curves in the Euclidean space.
Journal of Singularities. Vol. 21 (2020), 50--69. DOI: 10.5427/jsing.2020.21c
[46] (with S. Honda)
Evolutes and focal surfaces of framed immersions in the Euclidean space.
Proceedings of the Royal Society of Edinburgh Section A: Mathematics. Vol. 150 (2020), 497--516. DOI: 10.1017/prm.2018.84
[45] (with K. Teramoto)
Surfaces of revolution of frontals in the Euclidean space.
Bulletin of the Brazilian Mathematical Society, New Series. Vol. 51 (2020), 887--914. DOI: 10.1007/s00574-019-00180-x
[44] (with D. Pei and H. Yu)
Envelopes of one-parameter families of framed curves in the Euclidean space.
Journal of Geometry. Vol. 110 (2019), 31pp. DOI: 10.1007/s00022-019-0503-1
[43] (with S. Honda and S. Izumiya)
Developable surfaces along frontal curves on embedded surfaces.
Journal of Geometry. Vol. 110 (2019), 20pp. DOI: 10.1007/s00022-019-0485-z
[42]
Envelopes of families of Legendre mappings in the unit tangent bundle over the Euclidean space.
Journal of Mathematical Analysis and Applications. Vol. 473 (2019), 408--420. DOI: 10.1016/j.jmaa.2018.12.057
[41] (with T. Fukunaga)
Framed surfaces in the Euclidean space.
Bulletin of the Brazilian Mathematical Society, New Series. Vol. 50 (2019), 37--65. DOI:10.1007/s00574-018-0090-z
[40] (with S. Izumiya and H. Teramoto)
Geometric equivalence among smooth map germs.
Methods and Applications of Analysis. Vol. 25 (2018), 337--362. DOI: 10.4310/MAA.2018.v25.n4.a5
[39] (with S. Izumiya and M.C. Romero-Fuster)
Evolutes of curves in the Lorentz-Minkowski plane.
Advanced Studies in Pure Mathematics. Vol. 78 (2018), 313--330. DOI:10.2969/aspm/07810313
[38] (with Y. Li, D. Pei and H. Yu)
Envelopes of Legendre curves in the unit spherical bundle over the unit sphere.
The Quarterly Journal of Mathematics. Vol. 69 (2018), 631--653. DOI:10.1093/qmath/hax056
[37] (with T. Fukunaga)
Existence conditions of framed curves for smooth curves.
Journal of Geometry. Vol. 108 (2017), 763--774. DOI:10.1007/s00022-017-0371-5
[36]
Envelopes of Legendre curves in the unit tangent bundle over the Euclidean plane.
Results in Mathematics. Vol. 71 (2017), 1473--1489. DOI:10.1007/s00025-016-0619-7
[35]
Legendre curves in the unit spherical bundle over the unit sphere and evolutes.
Contemporary Mathematics. Vol. 675 (2016), 337--355. DOI: 10.1090/conm/675/13600
[34] (with G. Ishikawa and Y. Machida)
Dn-geometry and singularities of tangent surfaces.
RIMS Kôkyûroku Bessatsu. B55 (2016), 67--87.
[33] (with S. Honda)
Framed curves in the Euclidean space.
Advances in Geometry. Vol. 16 (2016), 265--276. DOI: 10.1515/advgeom-2015-0035
[32] (with T. Fukunaga)
On convexity of simple closed frontals.
Kodai Mathematical Journal. Vol. 39 (2016), 389--398. DOI: 10.2996/kmj/1467830145
[31] (with G. Ishikawa and Y. Machida)
Singularities of tangent surfaces in Cartan's split G2-geometry.
Asian Journal of Mathematics. Vol. 20 (2016), 353--382. DOI: 10.4310/AJM.2016.v20.n2.a6
[30] (with L. Chen)
Dualities and evolutes of fronts in hyperbolic 2-space and de Sitter 2-space.
Journal of Mathematical Analysis and Applications. Vol. 437 (2016), 133--159. DOI: 10.1016/j.jmaa.2015.12.029
[29] (with T. Fukunaga)
Involutes of fronts in the Euclidean plane.
Beiträge zur Algebra und Geometrie. Vol. 57 (2016), 637--653. DOI: 10.1007/s13366-015-0275-1
[28] (with T. Fukunaga)
Evolutes and involutes of frontals in the Euclidean plane.
Demonstratio Mathematica. Vol. 48 (2015), 147--166. DOI: 10.1515/dema-2015-0015
[27] (with G. Ishikawa and Y. Machida)
Geometry of D4 conformal triality and singularities of tangent surfaces.
Journal of Singularities. Vol. 12 (2015), 27--52. DOI: 10.5427/jsing.2015.12c
[26]
Classifications of completely integrable implicit second order ordinary differential equations.
Journal of Singularities. Vol. 10 (2014), 271--285.
[25] (with T. Fukunaga)
Evolutes of fronts in the Euclidean plane.
Journal of Singularities. Vol. 10 (2014), 92--107.
[24] (with T. Fukunaga)
Existence and uniqueness for Legendre curves.
Journal of Geometry. Vol. 104 (2013), 297--307.
[23]
Completely integrable implicit ordinary differential equations.
Yokohama Mathematical Journal. Vol. 58 (2012), 17--29.
[22] (with S. Izumiya)
Pedal foliations and Gauss maps of hypersurfaces in Euclidean space.
Journal of Singularities. Vol. 6 (2012), 84--97.
[21] (with S. Izumiya)
On caustics of submanifolds and canal hypersurfaces in Euclidean space.
Topology and its Applications. Vol. 159 (2012), 501--508.
[20] (with G. Ishikawa and Y. Machida)
Asymmetry in singularities of tangent surfaces in contact-cone Legendre-null duality.
Journal of Singularities. Vol. 3 (2011), 126--143.
[19] (with S. Izumiya and F. Tari)
Folding maps on spacelike and timelike surfaces and duality.
Osaka Journal of Mathematics. Vol. 47 (2010), 839--862.
[18] (with S. Izumiya and K. Saji)
Horospherical flat surfaces in Hyperbolic 3-space.
Journal of the Mathematical Society of Japan. Vol. 62 (2010), 789--849.
[17]
A sufficient condition that contact equivalence implies right equivalence for smooth function germs.
Houston Journal of Mathematics. Vol. 35 (2009), 829--833.
[16] (with S. Izumiya)
Caustics and wave front propagations: Applications to differential geometry.
Banach Center Publications. Geometry and topology of caustics. Vol. 82 (2008), 125--142.
[15] (with Y. Machida)
Classifications of implicit second order ordinary differential equations of Clairaut type.
The Royal Society of Edinburgh Proceedings A (Mathematics). Vol. 138A (2008), 821--842.
[14] (with K. Saji)
Singularities of smooth mappings with patterns.
Proceedings of the Royal Society of Edinburgh: Section A Mathematics. Vol. 137 (2007), 415--430.
(available in Hokkaido University Preprint Series in Mathematics No. 755.)
[13]
On complete solutions and complete singular solutions of second order ordinary differential equations.
Colloquium Mathematicum. Vol. 109 (2007), 271--285.
[12] (with S. Izumiya)
Spacelike Parallels and Evolutes in Minkowski pseudo-spheres.
Journal of Geometry and Physics. Vol. 57 (2007), 1569--1600.
[11]
On completely integrable first order ordinary differential equations.
Proceedings of the Australian-Japanese Workshop on Real and Complex singularities. (2007), 388--418.
[10]
On implicit second order ordinary differential equations: Completely integrable and Clairaut type.
Journal of Dynamical and Control Systems. Vol. 13 (2007), 273--288.
[9]
Bifurcations of holonomic systems of general Clairaut type.
Hokkaido Mathematical Journal. Vol. 35 (2006), 905--934.
[8] (with S. Izumiya and M. Kikuchi)
Global properties of spacelike curves in Minkowski 3-space.
Journal of Knot theory and its Ramifications. Vol. 15 (2006), 869--881.
[7]
Bifurcations of completely integrable first order ordinary differential equations. (in Russian)
Sovrem. Mat. Prilozh. Vol.33 (2005), 110--125. translation in Journal of Mathematical Sciences Vol. 144 (2007), 3854-3869.
[6] (with S. Izumiya, D. Pei and M.C. Romero-Fuster)
The horospherical geometry of Submanifolds in Hyperbolic space.
Journal of the London Mathematical Society. Vol. 71 (2005), 779--800.
[5]
Holonomic systems of general Clairaut type.
Hokkaido Mathematical Journal. Vol. 34 (2005), 247--263.
[4] (with S. Izumiya, D. Pei and M.C. Romero-Fuster)
On the horospherical ridges of submanifolds of codimension 2 in Hyperbolic n-space.
Bulletin of Brazilian Mathematical Society. Vol. 35 (2004), 177--198.
[3] (with S. Izumiya and D. Pei)
Singularities of evolutes of hypersurfaces in Hyperbolic space.
Proceedings of the Edinburgh Mathematical Society. Vol. 47 (2004), 131--153.
[2] (with S. Izumiya and D. Pei)
Curves and Surfaces in Hyperbolic space.
Banach Center Publications. Geometric Singularity Theory. Vol. 65 (2004), 107--123.
[1]
Bifurcations of ordinary differential equations of Clairaut type.
Journal of Differential Equations. Vol. 190 (2003), 579--599.
講究録
[3]
Evolutes and involutes of fronts in the Euclidean plane. 数理解析研究所講究録1868. (2013), 83--100.
[2]
Caustics and wave front propagations. 数理解析研究所講究録1707. (2010), 135--148.
[1]
微分幾何学と特異点論. 数理解析研究所講究録1623. (2009), 35--53.