Paper

• Classification of non-degenerate regular polyhedral complexes of positive curvature
  Fumiko Ohtsuka, Department of Mathematics, Faculty of Science
  Mathematical Journal of Ibaraki University, 2024, [Reviewed]
• 〔Major achievements〕Some geometric properties of regular polyhedral complexes
  Fumiko Ohtsuka
  Math. J. Ibaraki Univ., Aug. 2022, [Reviewed]
• Structure of 2-skeletons of higher dimensional regular polytopes　　　　　　　　　　　　　　　
  Fumiko Ohtsuka
  Math. J. Ibaraki Univ., 2018, [Reviewed]
• A natural generalization of regular convex polyhedra
  Jin-ichi Itoh; Fumiko Ohtsuka, Lead, As a natural generalization of surfaces of Platonic solids, we define a class of polyhedra, called simple regular polyhedral BP-complexes, as a class of 2-dimensional polyhedral metric complexes satisfying certain conditions on their vertex sets, and we give a complete classification of such polyhedra. They are either the surface of a Platonic solid, a p-dodecahedron, a p-icosahedron, an m-covered regular n-gon for some m >= 2 or a complete tripartite polygon. (C) 2017 Elsevier B.V. All rights reserved., ELSEVIER SCIENCE BV
  TOPOLOGY AND ITS APPLICATIONS, Mar. 2017, [Reviewed]
• Some remarks on simple closed geodesics of surfaces with ends
  Jin-ichi Itoh; Fumiko Ohtsuka and Tudor Zamfirescu, Lead, If a non-compact complete surface M is not homeomorphic to a subset of the plane or of the projective plane, then it has infinitely many simple closed geodesics [7]. In this paper, we consider simple closed geodesics on a surface homeomorphic to such a subset., SOC MATEMATICE ROMANIA
  Bull. Math. Soc. Sci. Math. Roumanie, 2009, [Reviewed]
• Total curvature of noncompact piecewise Riemannian 2-polyhedra
  Jin-ichi Itoh; Fumiko Ohtsuka, Lead, Institute of Mathematics, University of Tsukuba
  Tsukuba J. Math., 2005, [Reviewed]
• Erratum to: "Structure of flat piecewise Riemannian 2-polyhedra"
  Fumiko Ohtsuka, The object of our research is a piecewise Riemannian 2-polyhedron which is a combinatorial 2-polyhedron such that each 2-simplex is isometric to a triangle bounded by three smooth curves on some Riemannian 2-manifold. In the previous paper [4], which is a joint work with J. Itoh, we have introduced the concept of total curvature for piecewise Riemannian 2-polyhedra and proved a generalized Gauss-Bonnet theorem and a generalized Cohn-Vossen theorem. In this paper, we shall give a definition of flatness of piecewise Riemannian 2-polyhedra and characterize them., Faculty of Science, Ibaraki University
  Math. J. Ibaraki Univ., 2005
• Structure of flat piecewise Riemannian 2-polyhedra
  Fumiko Ohtsuka, The object of our research is a piecewise Riemannian 2-polyhedron which is a combinatorial 2-polyhedron such that each 2-simplex is isometric to a triangle bounded by three smooth curves on some Riemannian 2-manifold. In the previous paper [4], which is a joint work with J. Itoh, we have introduced the concept of total curvature for piecewise Riemannian 2-polyhedra and proved a generalized Gauss-Bonnet theorem and a generalized Cohn-Vossen theorem. In this paper, we shall give a definition of flatness of piecewise Riemannian 2-polyhedra and characterize them., Faculty of Science, Ibaraki University
  Math. J. Ibaraki Univ., 2004, [Reviewed]
• Total excess on length surfaces
  Yoshiroh Machigashira; Fumiko Ohtsuka, Corresponding, We study the space of directions on a length space and examine examples having particular spaces of directions. Then we generalize the notion of total excess on length spaces satisfying some suitable conditions, which we call good surfaces. For good surfaces we generalize the Euler characteristic, and prove the generalized Gauss-Bonnet Theorem and other relations between the total excess and the Euler characteristic. Furthermore, we see that the Gaussian curvature can be defined almost everywhere on a good surface with non-positive total excess., SPRINGER-VERLAG
  Mathematische Annalen, 2001, [Reviewed]
• Total excess and Tits metric for piecewise Riemannian 2-manifolds
  Kazuhiro Kawamura; Fumiko Ohtsuka, Lead, A piecewise Riemannian 2-manifold is a combinatorial 2-manifold with a triangulation such that each 2-simplex is a geodesic triangle of some Riemannian 2-manifold. In this paper, we study the total excess e(X) of a simply connected nonpositively curved piecewise Riemannian 2-manifold X in connection with the Tits metric on the boundary at infinity X(infinity). (C) 1999 Elsevier Science B.V. All rights reserved., ELSEVIER SCIENCE BV
  Topology and its Applications, 1999, [Reviewed]
• The existence of a straight line of piecewise Riemannian 2-manifolds　　　　　　　　　　　　　　　
  Kazuhiro Kawamura; Fumiko Ohtsuka, Lead
  Note di Matematica, 1998, [Reviewed]
• Hausdorff approximations on Hadamard manifolds and their ideal boundaries　　　　　　　　　　　　　　　
  Fumiko Ohtsuka
  Tsukuba Journal of Mathematics, 1996, [Reviewed]
• Rigidity of compact ideal boundaries of manifolds joined by Hausdorff approximations
  Fumiko Ohtsuka, The concept of ideal boundary of Hadamard monifolds was introduced by Eberlein and O'Neill [3] in 1973, which had marked a millestone is the study of the geometry of noncompact Reimannian manifolds. Since then, it has been utilized in various fields of research on Hadamard manifolds. ..., University of Tsukuba
  Tsukuba Journal of Mathematics, 1994, [Reviewed]
• The Euclidean factor of a Hadamard manifold
  Toshiaki Adachi; Fumiko Ohtsuka, The ideal boundary X(infinity) of a Hadamard manifold X is the set of asymptotic classes of rays on X. We shall characterize the Euclidean factor of X by information on X(infinity). Under the assumption that the diameter of X(infinity) is pi, we call a boundary point that has a unique point of Tits distance pi a polar point. We shall show that such points form a standard sphere and compose the boundary of the Euclidean factor of the given Hadamard manifold., AMER MATHEMATICAL SOC
  Proceedings of the American mathematical Society, 1991, [Reviewed]
• On manifolds having some restricted ideal boundaries
  Fumiko Ohtsuka, The theory of the ideal boundary has arisen as a method of a study of noncompact manifolds. In this paper we shall investigate properties of manifolds whose ideal boundaries satisfy some conditions related to the Tits metric. In Section 2 we shall consider in what conditions the Tits topology is equivalent to the sphere topology and in Section 3 the property of points at infinity which characterize the R-factor. Furthermore, in Section 4 we shall give a sufficient condition for a projective map PHI to be isometric., KLUWER ACADEMIC PUBL
  Geometriae Dedicata, 1991, [Reviewed]
• On a relation between the total curvature and Tits metric
  Fumiko Ohtsuka, Faculty of Science, Ibaraki University
  Bulletin of the Faculity of Science, Ibaraki University, Series A, 1988, [Reviewed]
• On the existence of a straight line
  Fumiko Ohtsuka, University of Tsukuba
  Tsukuba Journal of Mathematics, 1988, [Reviewed]
• Complete 2-transnormal hypersurfaces in a kaehler manifold of negative constant holomorphic sectional curvature
  Fumiko Ohtsuka, University of Tsukuba
  Tsukuba Journal of Mathematics, 1987, [Reviewed]
• Compact 2-transnormal hypersurface in a kaehler manifold of constant holomorphic sectional curvature
  Fumiko Ohtsuka, University of Tsukuba
  Tsukuba Journal of Mathematics, 1986, [Reviewed]