• Nonlinear Functional Analysis and Applications
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• v.29 no.1
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• pp.295-306
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• 2024

In this work, we investigate the generalized Hyers-Ulam stability of quadratic functional inequality in modular spaces satisfying ∆₂-conditions and Fatou property, and in 𝛽-homogeneous Banach spaces.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.1061-1066
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• 1996

We will give an example which is a normal Hausdorff countable dense homogeneous space but not a densely homogeneous space. Next, we will give a proof for the fact that every nondegenerate component of densely homogenous spaces is open and densely homogeneous.

• Kyungpook Mathematical Journal
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• v.52 no.1
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• pp.1-11
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• 2012

Our attention is turned to four-dimensional pseudo-Riemannian naturally reductive homogeneous spaces. In particular, our study leads to a complete classification of them.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.195-203
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• 2023

Special examples of harmonic manifolds that are not symmetric, proving that the conjecture posed by Lichnerowicz fails in the non-compact case have been intensively studied. We completely classify homogeneous structures on Damek-Ricci spaces equipped with the left invariant metric.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.825-832
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• 2011

In this paper, we make a minute and detailed proof of a part which is omitted in the process of obtaining the value of the curvature tensor for an invariant affine connection at the point {H} of a reductive homogeneous space G/H in the paper 'Invariant affine connections on homogeneous spaces' by K. Nomizu.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1229-1240
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• 2017

This paper presents a systematic study of the abstract harmonic analysis over spaces of complex measures on homogeneous spaces of compact groups. Let G be a compact group and H be a closed subgroup of G. Then we study abstract harmonic analysis of complex measures over the left coset space G/H.

• Honam Mathematical Journal
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• v.41 no.3
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• pp.609-617
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• 2019

We characterize two-point homogeneous spaces M by means of the structural operator $h={\frac{1}{2}}{\mathcal{L}}_{\xi}{\phi}$ or the characteristic Jacobi operator ${\ell}=R({\cdot},{\xi}){\xi}$ on the unit tangent sphere bundles $T_1M$.

• Honam Mathematical Journal
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• v.44 no.4
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• pp.636-645
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• 2022

We find a 1-parameter family of homogeneous structure tensors on contact hypersurfaces in Hermitian symmetric spaces. Among their associated Ambrose-Singer connections, we prove that the TanakaWebster connection is the unique pseudo-homothetically invariant connection.

• Journal of the Korean Mathematical Society
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• v.50 no.5
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• pp.1033-1050
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• 2013

We show the existence of smooth isolated curves of different degrees and genera in Calabi-Yau threefolds that are complete intersections in homogeneous spaces. Along the way, we classify all degrees and genera of smooth curves on BN general K3 surfaces of genus ${\mu}$, where $5{\leq}{\mu}{\leq}10$. By results of Mukai, these are the K3 surfaces that can be realised as complete intersections in certain homogeneous spaces.

• Journal of the Korean Mathematical Society
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• v.41 no.6
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• pp.1101-1114
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• 2004

We generalize a result of Dror Farjoun and Zabrodsky on the relationship between fixed point sets and homotopy fixed point sets, which is related to the generalized Sullivan Conjecture. As an application, we discuss extension problems considering actions on homogeneous spaces of p-compact groups.