Geometric structures on submanifolds in space forms and differential equations related to their structures.

(1)Suyama在研究一般共形平坦超曲面方面取得了显著的成果。自E.嘉当Suyama和Hertrich-Jeromin（巴斯大学）用循环Guichard网构造了所有共形平坦超曲面，并利用共形等价给出了它们的完全分类。这一工作从可积系统的观点出发，对高维子流形的研究有了新的发展。(2)Shiohama研究了曲积流形的径向曲率与拓扑之间的关系。他给出了各种测地线三角形的亚历山德罗夫-托波诺戈夫比较定理，并将其应用于翘曲积流形的分类。(3)Kurose研究了构造非正常仿射超球面的方法，给出了一个新的表示公式，并对由该公式得到的非正常仿射超曲面类进行了刻画。(4)黑濑和藤冈将与Burgers族可积方程相关的复双曲线中曲线的运动表示为Hamilton系统。(5)Kawakubo在三维空间形式中研究了Kirchhoff弹性杆，并得到了它们的显式公式。他还证明了克希霍夫弹性杆的能量泛函满足帕莱-斯梅尔条件。所得结果为研究封闭克希霍夫弹性杆的稳定性提供了一种有效的方法。(6)松浦研究离散化的曲线和曲面与理论的离散可积系统。他对离散的KdV方程作了几何解释，因此他成功地提出了一个非自治的版本。

(1) Suyama obtained remarkable results in the research on generic conformally flat hypersurfaces. The subject is an open problem since the work by E. Cartan. Suyama and Hertrich-Jeromin (Bath Univ.) constructed all conformally flat hypersurfaces with cyclic Guichard net and gave a complete classification of them by conformal equivalence. This work gives new development in the research on higher dimensional submanifolds from the integrable system view-points.(2) Shiohama studied the relation between radial curvature and topology of warped product manifolds. He gave Alexandrov-Toponogov comparison theorem for various geodesic triangles, and applied it for a classification of warped product manifolds.(3) Kurose studied the method of constructing improper affine hyperspheres and gave a new representation formula and a characterization of the class of improper affine hypersurfaces obtained by this formula.(4) Kurose and Fujioka gave a representation as a Hamiltonian system to the motions of curves in a complex hyperbola associated with the integrable equations of the Burgers hierarchy.(5) Kawakubo studied Kirchhoff elastic rods in three-dimensional space forms, and obtained the explicit formulas for them. Also, he proved that the energy functional for Kirchhoff elastic rods satisfies the Palais-Smale condition. The result gives an effective method of studying the stability of closed Kirchhoff elastic rods.(6) Matsuura studied discretizations of curves and surfaces in connection with the theory of discrete integrable systems. He made a geometric interpretation of the discrete KdV equation, so that he successfully proposed a non-autonomous version of it.