Publications

Recent papers:

  1. Hamiltonian non-displaceability of Gauss images of isoparametric hypersurfaces, Bull. London Math. Soc. 48 (5): 802-812 (2016)click here
  2. Stability of complete minimal Lagrangian submanifold and L2 harmonic 1-forms; Real and Complex Submanifolds, PROMS 106 (2014) 89-95 click here
  3. Errata of “Isoparametric hypersurfaces with (g, m) = (6, 2)”; Annals of Math. vol 183 (2016) 1057-1071 click here
  4. Remarks on the Dorfmeister-Neher theorem on isoparametric hypersurfaces; Osaka J. Math. 52 (2015) 373-377 click here
  5. Isoparametric hypersurfaces with (g,m)=(6,2); Annals of Math. vol.177(2013), 53-110. click here
  6. Moment maps of the spin action and the Cartan-Muenzner polynomials of degree four; Math. Ann. vol.355(2013), 1067-1084. click here
  7. Transnormal functions on a Riemannian manifold. DGA vol.31(2013), 130-139. click here
  8. Geometry of G2 orbits and isoparametric hypersurfaces; Nagoya Math. J. 203 (2011), 175-189. click here
  9. The Bryant-Salamon G2 manifolds and hypersurface geometry; click here (2006).

Publication list:

  1. Dorfmeister-Neher's theorem on isoparametric hypersurfaces;
    Osaka J. Math. 46, (2009) 695--715. click here
  2. The Gauss map of pseudo-algebraic minimal surfaces (with Y. Kawakami and R. Kobayashi);
    Forum Mathematicum. 20, (2008) 1055-1069. click here
  3. Isoparametric geometry and related fields
    Adv.Studies in Pure Math. 51, (2008) 305-326
  4. Classification of isoparametric hyeprsurfaces with 4 principal curvatures by T. E. Cecil, Q. S. Chi, G. R. Jensen; (in Japanese), Sugaku 58 No.3 (2006) 225--238. pdf
  5. Isoparametric hypersurfaces, revisited;
    Sugaku expositions; 17 (2004) 185-202. (Japanese in Sugaku 53 (2001) 18-33)
  6. Submanifolds with degenerate Gauss mappings in the spheres (with G. Ishikawa, M. Kimura);
    Adv. Studies in Pure Math., 37 (2002) 115-149.
  7. A global correspondence between CMC-surfaces in S3 and pairs of non-conformal harmonic maps into S2 (with R. Aiyama, K. Akutagawa and M. Umehara);
    Proc. Amer. Math. Soc. 128 (2000) 939-941.pdf
  8. The splitting and deformations of the generalized Gauss map of compact CMC surfaces;
    Tôhoku Math. J. 51 (1999) 35-53. pdf
  9. Hypersurface geometry and Hamiltonian systems of hydrodynamic type;
    Lobachevskii J. Math. 3 (1999) 209-220.
  10. The family of isometric superconformal harmonic maps and the affine Toda equations;
    J. Reine Angew. Math. 481 (1996) 1-25.
  11. On a complete minimal surface whose Gauss map misses two points (with Katsunori Sato);
    Archiv der Mathematik, 63, (1994) 565-576.
  12. Book review ``Lie Sphere Geometry'' (T. E. Cecil)
    Sugaku 46 (1994) 87-90.
  13. L2-harmonic 1-forms on a complete stable minimal hypersurface;
    Geometry and Global Analysis (ed. by T. Kotake, S. Nishikawa, R. Schoen), (1993) 289-294.
  14. Isotropy subgroup of G2/SO(4), the Hopf fibering and isoparametric hypersurfaces;
    Osaka J. of Math. 30 (1993) 179-202.pdf
  15. A note on Lie contact manifolds;
    Adv. Studies in Pure Math. 22 (1993) 169-187.
  16. A note on Ogiue-Takagi conjecture on euclidean 2-spheres (with Nobuko Takeuchi);
    Mem. Fac. Sci. Kyushu Univ. 46 (1992) 129-135.
  17. Lie contact structures and conformal structures;
    Kodai Math. J. 14 (1991) 42-71 (1991). pdf
  18. Lie contact structures and normal Cartan connections;
    Kodai Math. J. 14 (1991) 13-41.pdf
  19. Construction of taut embeddings and Cecil-Ryan conjecture (with Tetsuya Ozawa);
    Geometry of Manifolds (ed. by K. Shiohama), Acad. Press, (1989) 181-189.
  20. Dupin hypersurfaces with six principal curvatures;
    Kodai Math. J. 12 (1989) 308-315.pdf
  21. Dupin hypersurfaces and a Lie invariant;
    Kodai Math. J. 12 (1989) 228-256.pdf
  22. Correction of complete hypersurfaces in the space form with three principal curvatures;
    Bol. Soc. Brazil. Mat. 18 (1987) 83--94.
  23. Taut embeddings and Dupin hypersurfaces;
    Differential Geometry in Submanifolds, Lect. Notes in Math. 1090 (1984) 15-23.
  24. Compact Dupin hypersurfaces with three principal curvatures;
    Math. Zeit. 187 (1984) 433-452.click here
  25. Complete hypersurfaces in the space form with three principal curvatures;
    Math. Zeit. 179 (1982) 345-354.click here
  26. Minimal hypersurfaces in the space form with three principal curvatures;
    Math. Zeit. 170 (1980) 137-151.click here
  27. Some results on minimal surfaces with the Ricci condition;
    Minimal Submanifolds and Geodesics (ed. by M. Obata), Kaigai Pub. Ltd. (1978) 121-142.
  28. Certain hypersurfaces in the euclidean sphere;
    Kodai Math. Sem. Rep. 28 (1976) 9-18. click here

Proceedings and surveys:

  1. Hamiltonian Non-displaceability of the Gauss Images of Isoparametric Hypersurfaces (A survey), Hermitian-Grassmannian Submanifolds (Daegu, Korea, Jul. 2016), 83--99, Springer.
  2. Stability of Complete Minimal Lagrangian Submanifolds and L^2-Harmonic 1-forms, (joint work with S. Ueki), Real and Complex Submanifolds (Daejeon, Korea, Aug. 2014), 89--95, Springer.
  3. Homogeneity of isoparameric hypersurfaces with six principal curvatures; Oberwolfach Report NO.21/2010 (2010) 55-58
  4. Topologuy of the Bryant-Salamon G_2 manifolds and and some Ricci flat manifolds;
    RIMS Kokyuroku 1502 (2006) 230--237.
  5. Gauss map of pseudo-algebraic minimal surfaces;
    RIMS Kokyuroku 1460 (2005) 72-88.
  6. The Gauss map and the Nevanlinna theory;
    Proceedings of tenth international workshop on Differential Geometry, Kyungpook Univ. (2005) 35-38.
  7. G2 geometry from a view point of the hypersurface geometry;
    Proceedings of tenth international workshop on Differential Geometry, Kyungpook Univ. (2005) 31-34.
  8. On special Lagrangian submanifolds;
    RIMS Kokyuroku 1236 (2001) 1-8.
  9. The past and the present of isoparametric hypersurfaces —Élie Cartan and 21-st century—; (in Japanese)
    RIMS Kokyuroku 1206 (2001) 32-44.
  10. Achievement of Élie Cartan —commentary of an article by S. S. Chern and C. Chevaley;
    RIMS Kokyuroku 1206 (2001) 1-31.
  11. Submanifolds with degenerate Gauss mappings in the spheres (with G. Ishikawa, M. Kimura);
    Josai Mathematical Monograph, Differential Geometry 3 (2001) 125-138.
  12. Lie sphere geometry and Lie contact structure;
    RIMS Kokyuroku 1150 (2000) 143-146.
  13. Deformations and moduli of algebraic minimal surfaces (in Japanese);
    RIMS Kokyuroku 1113 (1999) 1-8.
  14. Construction of CMC surfaces in S3 from a pair of non-conformal harmonic maps into S2;
    Proceedings of DGA98(1998), Brno, Czecho (1999) 203-206.
  15. The splitting and deformations of the Gauss map of compact CMC surfaces;
    Proceedings of Brest Workshop 1997: Harmonic Morphism, Harmonic Maps and Related Topics (1999) 271-274.
  16. Introduction to ``Normalized Potentials of Minimal Surfaces in Spheres " (Q.S. Chi, L. Fernandez, H. Wu);
    Kofu Report; Integrable Systems and Related Topics 6 (1999) 27-31.
  17. On the theory of integrable systems and its applications;
    Proceedings of The Third International Workshop on Differential Geometry (1998), Kyungpook Univ., Korea, (1999) 41--55.
  18. Recent topics on harmonic map theory and related parts;
    Proceedings of The Third International Workshop on Differential Geometry (1998), Kyungpook Univ., Korea, (1999) 31-39.
  19. Poisson group actions and the inverse scattering theory in integrable systems;
    Kofu Report; Harmonic maps, Spectral curves and Soliton Equations 3 (1997) 1-82.
  20. Introduction to ``Dressing Actions of the Loop Groups on Constant Mean Curvature Surfaces" (H. Wu);
    Kofu Report; Harmonic maps, Submanifold Geometry and Integrable Systems 2 (1996) 70-88.

Books:

  1. Geometry of curved space (Blue Backs, Kodansha 2017, in Japanese)
  2. Introduction to modern geometry (SGC Library-124, Science Co., Ltd. 2016, in Japanese)
  3. R. Miyaoka (Eds): Su Buqing Lecture Note Series No.1 (2011) Tohoku Math. Publ. 35 181 pages
  4. M. Guest, R. Miyaoka, Y. Ohnita, W. Rossman (Eds): Riemann Surfaces Harmonic Maps and Visualization
    OCAMI Studies 13 (2010), 277 pages.
  5. M. Guest, R. Miyaoka, Y. Ohnita (Eds): Survey on Geometry and Integrable Systems
    Adv. Studies in Pure Math.51 (2008) 510 pages.
  6. R. Miyaoka,M. Kotani (Eds) Mathematics in the 21st century —unscaled peaks of geometry—
    Nihon Hyoron-sha (2004) 438 pages.
  7. R. Miyaoka,H. Tamaru(Eds): Theory of Lie Groups and Manifolds,
    Sugaku Kokyuroku, Sophia Univ.(No. 45)(2003) 136 pages.
  8. M. Guest, R. Miyaoka, Y. Ohnita (Eds): DIFFERENTIAL GEOMETRY AND INTEGRABLE SYSTEMS,
    CONTEMPORARY MATHEMATICS vol. 308 (2002) 349 pages.
  9. M. Guest, R. Miyaoka, Y. Ohnita (Eds): INTEGRABLE SYSTEMS, TOPOLOGY, AND PHYSICS,
    CONTEMPORARY MATHEMATICS vol. 309 (2002) 324 pages.

Surveys in Japanese:

  1. Coffee Break:Sugaku Seminar (2012.5)
  2. Minimal surfaces and Variational problems : Suri-Kagaku (2010)
  3. Progress in Surface Theory (Workshop in Oberwolfach) : Suri-Kagaku (2010)
  4. Harmonic maps and symmetric spaces : Sophia 199 (Sophia Univ.)(2001) 123--131.
  5. Start of learning ; Sugaku no Tanoshimi 25 (2001) 9-15, Nihon Hyoron-sha,Book : Sugaku manabihajime No.2.
  6. What is the geometry of hypersurfaces?; Sugaku no Tanoshimi 13 (1999) 96-108, Nihon hyoron-sha,Book : Perspective of modern mathematics (2001) 178-193.
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