[1] Ahara, K., 6 dimensional almost complex $S^1$ manifolds with $\chi(M)=4$, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 38 (1991),47-72. [2] Ahara, K. and Hattori, A., [[4 dimensional symplectic $S^1$-manifolds admitting moment map>https://dl.dropbox.com/u/72818967/Ahara-Hattori.pdf]], J. Fac. Sci. Univ. Tokyo Sect. IA Math. 38 (1991),251-298 . [3] Ahara, K., Ikeda, K. and Ishimura, N., Linear discrete model for shortening polygons, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 39 (1992), 365-378 . [4] Ahara, K. and Ishimura, N., On the Mean Curvature Flow of Thin Doughnuts, Lecture Notes in Num. Appli. Anal., 12 (1993), 1-33 . [5] Ahara, K., On the Topology of Fermat Type Surface of Degree 5 and the Numerical Analysis of Algebraic Curves, Tokyo J. of Math., 16,(1993), 321-340. [6] Ahara, K., A short note on Hattori's conjecture for Grassmann manifolds., Memoirs of inst. of sci. and tech. Meiji Univ. , 32 (1993),83-98. [7] Ahara, K., Topology of Algebraic curves and a computer software 'Mr. Monomie', (Japanese), Memoirs of inst. of sci. and tech. Meiji Univ., 34, (1995),19-46. [8] Ahara, K., Yamada Kinji, Shapes of Hexagrams, J. Math. Sci. Univ. Tokyo 6 (1999), 539-558 Preprints [P1] Ahara, K., The numerical analysis of an energy of a knot., preprint (1992) [P2] Ahara, K., Combinatorial hyperbolic curve-shortening , preprint (1997). [P3] Ahara, K., Combinatorial hyperbolic curve-shortening II, preprint (1998).