• Journal of the Chungcheong Mathematical Society
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• v.22 no.1
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• pp.65-71
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• 2009

Let f be an 2-isometry on a non-Archimedean 2-normed space. In this paper, we prove that the barycenter of triangle is invariant for f up to the translation by f(0), in this case, needless to say, we can imply naturally the Mazur-Ulam theorem in non-Archimedean 2-normed spaces.

• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.771-782
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• 2019

We show that mappings preserving unit distance are close to two-isometries. We also prove that a mapping f is a linear isometry up to translation when f is a two-expansive surjective mapping preserving unit distance. Then we apply these results to consider two-isometries between normed spaces, strictly convex normed spaces and unital $C^*$-algebras. Finally, we propose some remarks and problems about generalized two-isometries on Banach spaces.

• Honam Mathematical Journal
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• v.46 no.2
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• pp.249-266
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• 2024

In this work, we study time-like and space-like surfaces invariant by a group of translation isometries of the half-space model ℋ³₁ of the anti-de Sitter space ℍ³₁ . We determine all such surfaces with constant mean curvature and constant Gaussian curvature. We also obtain umbilical surfaces of ℋ³₁.

• Journal of the Korea Computer Graphics Society
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• v.3 no.2
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• pp.55-63
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• 1997

This paper presents a method of detecting motion isometry from the motions of two objects in a three-dimensional space. We define the motion isometry based on the group theory and a newly defined coordinate system. Motion isometry can be detected using the coordinate system which we call Motion Specific Coordinate System(MSCS). In addition, we present an algorithm if two motions are isometric using the coordinate system. The algorithm can detect the difference in the motions of objects irrespective of their positions or the directions of their motions in a space. The algorithm can also detect the motion difference in the case of segmented objects which have several joints. The motion quantity is represented by translation values or rotation angles about some axes.