• Communications of the Korean Mathematical Society
• /
• v.13 no.4
• /
• pp.817-823
• /
• 1998

In the present paper, we study conformal and projective Killing vector fields and infinitesimal Q-transformations on a quaternionic Kahlerian manifold, and prove that an infinitesimal conformal or projective automorphism in a compact quaternionic Kahlerian manifold is necessarily infinitesimal automorphism.

• Bulletin of the Korean Mathematical Society
• /
• v.59 no.1
• /
• pp.101-110
• /
• 2022

In this article, the notion of *-conformal Ricci soliton is defined as a self similar solution of the *-conformal Ricci flow. A Sasakian 3-metric satisfying the *-conformal Ricci soliton is completely classified under certain conditions on the soliton vector field. We establish a relation with Fano manifolds and proves a homothety between the Sasakian 3-metric and the Berger Sphere. Also, the potential vector field V is a harmonic infinitesimal automorphism of the contact metric structure.

• Korean Journal of Mathematics
• /
• v.29 no.3
• /
• pp.547-554
• /
• 2021

The object of the present paper is to characterize Sasakian 3-manifolds admitting a gradient Ricci-Yamabe soliton. It is shown that a Sasakian 3-manifold M with constant scalar curvature admitting a proper gradient Ricci-Yamabe soliton is Einstein and locally isometric to a unit sphere. Also, the potential vector field is an infinitesimal automorphism of the contact metric structure. In addition, if M is complete, then it is compact.

• Journal of the Korean Mathematical Society
• /
• v.37 no.2
• /
• pp.225-243
• /
• 2000

We explain the notion of complete system and how it naturally arises from the equivalence problem of G-structures. Then we construct a complete system of 3rd order for the infinitesimal CR automorphisms of CR manifold of nondegenerate Levi form.

• Journal of the Korean Mathematical Society
• /
• v.40 no.4
• /
• pp.695-708
• /
• 2003

We study the existence of solutions for overdetermined PDE systems that admit prolongation to a complete system. We reduce the problem to a Pfaffian system on a submanifold of the jet space of unknown functions and then express the integrability conditions in terms of the coefficients of the original system. As possible applications we present some local problems in CR geometry: determining the CR embeddibility into spheres and the existence of infinitesimal CR automorphisms.

• Journal of the Korean Mathematical Society
• /
• v.53 no.3
• /
• pp.489-501
• /
• 2016

In this paper, we study the rigidity under $K{\ddot{a}}hler$ deformation of the complex structure of odd Lagrangian Grassmannians, i.e., the Lagrangian case $Gr_{\omega}$(n, 2n+1) of odd symplectic Grassmannians. To obtain the global deformation rigidity of the odd Lagrangian Grassmannian, we use results about the automorphism group of this manifold, the Lie algebra of infinitesimal automorphisms of the affine cone of the variety of minimal rational tangents and its prolongations.

• Korean Journal of Mathematics
• /
• v.30 no.4
• /
• pp.643-652
• /
• 2022

In this paper, we will describe affine homogeneous domains in the complex plane. For this study, we deal with the Lie algebra of infinitesimal affine transformations, a structure of the hyperbolic metric involved with affine automorphisms. As a consequence, an affine homogeneous domain is affine equivalent to the complex plane, the punctured plane or the half plane.

• Bulletin of the Korean Mathematical Society
• /
• v.23 no.2
• /
• pp.167-170
• /
• 1986

Let M be a von Neumann algebra and .alpha., .betha. be *-automorphisms of M satisfying the operator equation .alpha.+.alpha.$^{-1}$ =.betha.+.betha.$^{-1}$ This operator equation has been extensively studied and many important decomposition theorems have been obtained by several authors (for instance see [4], [5], [2], [1]). Originally, this operator equation arose in the paper of Van Daele on the new approach of the Tomita-Takesaki theory in the case of modular operators ([7]). In the case of one-parameter automorphism groups, this equation has produced a bounded and completely positive map which can play a role similar to the infinitesimal generator (for details see [6] and [1]). A recent and one of the most important applications of this equation has been in developing an anglogue of the Tomita-Takesaki theory for Jordan algebras by Haagerup [3]. One general result of this theory is the following.