Research papers

・Strict convexity of hypersurfaces in spheres,
 J. Math. Sci. Univ. Tokyo 5 (1998) 423-433.

・Strict convexity of hypersurfaces in spheres, II,
 J. Math. Sci. Univ. Tokyo 6 (1999) 1-11.

・An isolated umbilical point of the graph of a homogeneous polynomial,
 Geom. Dedicata 82 (2000) 115-137.

・The behavior of the principal distributions around an isolated umbilical point,
 J. Math. Soc. Japan 53 (2001) 237-260.

・Umbilical points of the graphs of homogeneous polynomials of degree 3,
 J. Math. Sci. Univ. Tokyo 8 (2001) 71-87.

・The behavior of the principal distributions on the graph of a homogeneous polynomial,
 Tohoku Math. J. 54 (2002) 163-177.

・A class of real-analytic surfaces in the 3-Euclidean space,
 Tsukuba J. Math. 26 (2002) 251-267.

・The behavior of the principal distributions on a real-analytic surface,
 J. Math. Soc. Japan 56 (2004) 201-214.

・An umbilical point on a non-real-analytic surface,
 Hiroshima Math. J. 33 (2003) 1-14.

・Parallel curved surfaces,
 Tsukuba J. Math. 28 (2004) 223-243.

・A conjecture in relation to Loewner's conjecture,
 J. Math. Soc. Japan 57 (2005) 1-20.

・An isolated umbilical point of a Willmore surface,
 Osaka J. Math. 41 (2004) 865-876.

・Willmore surfaces in S^3 and minimal surfaces in S^4_1,
 Kumamoto J. Math. 18 (2005) 57-68.

・A two-dimensional Riemannian manifold with two one-dimensional distributions,
 Kyushu J. Math. 59 (2005) 285-299.

・Semisurfaces and the equations of Codazzi-Mainardi,
 Tsukuba J. Math. 30 (2006) 1-30.

・A surface which has a family of geodesics of curvature,
 Beitraege zur Algebra und Geometrie 48 (2007) 237-250.

・A family of surfaces in E^3 given by an over-determined system,
 Current Developments in Differential Geometry and its Related Fields, 57-75, World Scientific, 2016.

・Local characterizations of complex curves in C^2 and sphere Schwarz maps,
 Internat. J. Math. 27 (2016) 1650067 (16 pages)

・Over-determined systems in relation to principal curvatures,
 J. Geom. 108 (2017) 355-373.

・C^1-umbilics with arbitrarily high indices,
 Pacific J. Math. 288 (2017) 1-26 (joint work with Toshifumi Fujiyama and Masaaki Umehara).

・The geodesic curvatures of lines of curvature,
  preprint .

・Molding surfaces and Liouville's equation,
  preprint .

・Two generalizations of an over-determined system on a surface,
  preprint .

・Surfaces with zero mean curvature vector in 4-dimensional space forms,
  preprint .

・Complex curves and isotropic minimal surfaces in hyperK\"{a}hler 4-manifolds,
  preprint .

・Surfaces in pseudo-Riemannian space forms with zero mean curvature vector,
  preprint .