• Bulletin of the Korean Mathematical Society
• /
• v.54 no.6
• /
• pp.2029-2041
• /
• 2017

The main aim of this article is to study symmetric (v, k, ${\lambda}$) designs admitting a flag-transitive and point-primitive automorphism group G whose socle is PSU(3, q). We indeed show that such designs must be complete.

• Communications of the Korean Mathematical Society
• /
• v.35 no.2
• /
• pp.653-666
• /
• 2020

In this paper, when G is a connected and simply connected nilpotent Lie group of dimension less than or equal to four, we study the uniform lattices Γ of G up to isomorphism and then we study the structure of the automorphism group Aut(Γ) of Γ from the viewpoint of splitting as a natural extension.

• East Asian mathematical journal
• /
• v.8 no.2
• /
• pp.151-162
• /
• 1992

• Journal of the Korean Mathematical Society
• /
• v.21 no.1
• /
• pp.63-70
• /
• 1984

• East Asian mathematical journal
• /
• v.13 no.2
• /
• pp.265-269
• /
• 1997

• Journal of the Korean Mathematical Society
• /
• v.18 no.1
• /
• pp.81-87
• /
• 1981

• Journal of the Korean Mathematical Society
• /
• v.45 no.5
• /
• pp.1221-1241
• /
• 2008

Most of domains people have studied are convex bounded projective (or affine) domains. Edith $Soci{\acute{e}}$-$M{\acute{e}}thou$ [15] characterized ellipsoid in ${\mathbb{R}}^n$ by studying projective automorphism of convex body. In this paper, we showed convex and bounded projective domains can be identified from local data of their boundary points using scaling technique developed by several mathematicians. It can be found that how the scaling technique combined with properties of projective transformations is used to do that for a projective domain given local data around singular boundary point. Furthermore, we identify even unbounded or non-convex projective domains from its local data about a boundary point.

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.1
• /
• pp.109-115
• /
• 2020

Recently, Lesieutre constructed a 6-dimensional projective variety X over any field of characteristic zero whose automorphism group Aut(X) is discrete but not finitely generated. As an application, he also showed that X is an example of a projective variety with infinitely many non-isomorphic real structures. On the other hand, there are also several finiteness results of real structures of projective varieties. The aim of this short paper is to give a sufficient condition for the finiteness of real structures on a projective manifold in terms of the structure of the automorphism group. To be more precise, in this paper we show that, when X is a projective manifold of any dimension≥ 2, if Aut(X) does not contain a subgroup isomorphic to the non-abelian free group ℤ ∗ ℤ, then there are only finitely many real structures on X, up to ℝ-isomorphisms.

• Journal of applied mathematics & informatics
• /
• v.9 no.2
• /
• pp.859-867
• /
• 2002

In this paper, we get a necessary and sufficient condition for an inner automorphism between compact connected semisimple Lie groups to be an atone transformation, and obtain atone transformations of (SU(n),g) with some left invariant metric g.

• Communications of the Korean Mathematical Society
• /
• v.17 no.4
• /
• pp.635-645
• /
• 2002

Two examples of $\varepsilon$-famed manifolds are constructed. It is proved that an $\varepsilon$-framed structure on a manifold is not unique. Automorphism groups of r-framed manifolds are studied. Lastly we prove that a connected Lie group G admits a left invariant normal $\varepsilon$-framed structure if and only if the Lie algebra of all left invariant vector fields on G is an $\varepsilon$-framed Lie algebra.