[00172] On application of principle curvature distribution in local differential geometry
Session Time & Room : 1C (Aug.21, 13:20-15:00) @A508
Type : Proposal of Minisymposium
Abstract : Recently, shape has become increasingly crucial in device and materials science. In this symposium, we will focus on principal curvature distributions in differential geometry and discuss examples where the principal curvature distributions play a crucial role. We take particular note of the curved carbon nanotubes discovered in the 2000s, and the manufacturing methods of curved surfaces in shipbuilding and other applications. Both seem unrelated at first glance, but from an applied mathematical point of view, the principal curvature distribution is analyzed by utilizing common mathematics. This symposium aims to discuss these issues from the standpoint of local differential geometry.
Organizer(s) : Shigeki Matsutani, Yutaro Kabata, Yuta Ogata, Jun Onoe
[04166] Fullerene and discrete principal curvature
Format : Talk at Waseda University
Author(s) :
Shigeki Matsutani (Kanazawa University)
Yusuke Noda (Okayama Prefectural University)
Abstract : Due to geometrical investigations of the carbon configurations of the first principle computations, the novel symmetry in the fullerenes, i.e., the pre-constant discrete principal curvature (pCDPC) structure, was recently found.
In this talk, we show the symmetry mainly on the C60 polymers and related fullerenes from geometrical viewpoints.
[03759] Interplay between topology-induced geometry and the electronic properties of nanocarbon materials
Format : Talk at Waseda University
Author(s) :
Jun Onoe (Nagoya University)
Abstract : The quantum mechanics in curved surface has been studied in 1950s and predicted that the electron behaviors are affected by Gaussian and average curvatures theoretically in 1980s. We have first demonstrated the quantum mechanics in submanihold experimentally using one-dimensional periodic uneven structured C60 polymer formed by electron-beam irradiation of C60 film.
[04350] On discrete constant principal curvature surfaces
Format : Talk at Waseda University
Author(s) :
Yuta Ogata (Kyoto Sangyo University)
Abstract : In this talk, we will study the discrete surface theory on a full 3-ary oriented tree and introduce the notion of discrete principal curvatures on them. In order to investigate the geometric meaning of discrete principal curvatures, we will also define a discrete analog of curvature lines on discrete surfaces, called weak-curvature lines. At the end of the talk, we also show some examples of discrete constant principal curvature surfaces.
[04368] Surface parametrization for manufacturing by principal curvature integral
Format : Talk at Waseda University
Author(s) :
Yutaro Kabata (Nagasaki University)
Abstract : The choice of coordinates is crucial in the theory of curves and surfaces. In this presentation, we discuss the appropriate way to choose coordinates for curves and surfaces from a manufacturing perspective. Specifically, we define coordinates obtained from the integration of curvature for curves and principal curvatures for surfaces, and present results related to the stratification of curves and surfaces obtained from these coordinates.
