• 대한수학회보
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• 제47권4호
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• pp.815-823
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• 2010

Let ${\tau}\;{\neq}\;\delta_0$ be either a power bounded radial measure with compact support on the unit disc D with $\tau(D)\;=\;1$ such that there is a $\delta$ > 0 so that ${\mid}\hat{\tau}(s){\mid}\;{\neq}\;1$ for every $s\;{\in}\;\Sigma(\delta)$ \ {0,1}, or just a radial probability measure on D. Here, we provide a decomposition of the set X = {$h\;{\in}\;L^{\infty}(D)\;{\mid}\;lim_{n{\rightarrow}{\infty}}\;h\;*\;\tau^n$ exists}. Let $\tau_1$, ..., $\tau_n$ be measures on D with above mentioned properties. Here, we prove that if $f\;{in}\;L^{\infty}(D^n)$ satisfies an invariant volume mean value property with respect to $\tau_1$, ..., $\tau_n$, then f is n-harmonic.

• 대한수학회논문집
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• 제28권3호
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• pp.511-516
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• 2013

We establish an easy proof of an integral identity using the unitary invariance, which is applied to compare harmonicity and M-harmonicity.

• 대한수학회논문집
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• 제36권1호
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• pp.135-147
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• 2021

In this paper, we introduce the harmonicity of a covector field on a Riemannian manifold (M, g) to its cotangent bundle T∗ M equipped with g-natural metric. Afterward we also construct some examples of harmonic covector fields.

• 대한수학회지
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• 제51권5호
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• pp.881-895
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• 2014

In a recent paper [10] we introduced the notion of Levi harmonic map f from an almost contact semi-Riemannian manifold (M, ${\varphi}$, ${\xi}$, ${\eta}$, g) into a semi-Riemannian manifold $M^{\prime}$. In particular, we compute the tension field ${\tau}_H(f)$ for a CR map f between two almost contact semi-Riemannian manifolds satisfying the so-called ${\varphi}$-condition, where $H=Ker({\eta})$ is the Levi distribution. In the present paper we show that the condition (A) of Rawnsley [17] is related to the ${\varphi}$-condition. Then, we compute the tension field ${\tau}_H(f)$ for a CR map between two arbitrary almost contact semi-Riemannian manifolds, and we study the concept of Levi pluriharmonicity. Moreover, we study the harmonicity on quasicosymplectic manifolds.

• 호남수학학술지
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• 제36권3호
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• pp.543-553
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• 2014

The aim of this paper is to define hyperholomorphic functions with dual octonion variables on $\mathbb{C}^4{\times}\mathbb{C}^4$ in another way. Using condition of harmonicity, we research properties of functions of dual octonion variables in Clifford analysis.

• 호남수학학술지
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• 제36권4호
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• pp.921-932
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• 2014

The aim of this paper is to define hyperholomorphic functions with dual sedenion variables on $\mathcal{S}{\times}\mathcal{S}$, where $$\mathcal{S}{\sim_=}\mathbb{C}^8$$. By the condition of harmonicity, we research properties of hyperholomorphic functions of dual sedenion variables in Clifford analysis.

• 대한수학회보
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• 제59권2호
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• pp.375-395
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• 2022

We define an almost Norden submersion (holomorphic and semi-Riemannian submersion) between almost Norden manifolds and show that, in most of the cases, the base manifold has the similar kind of structure as that of total manifold. We obtain necessary and sufficient conditions for almost Norden submersion to be a totally geodesic map. We also derive decomposition theorems for the total manifold of such submersions. Moreover, we study the harmonicity of almost Norden submersions between almost Norden manifolds and between Kaehler-Norden manifolds. Finally, we derive conditions for an almost Norden submersion to be a harmonic morphism.

• 호남수학학술지
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• 제41권4호
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• pp.769-780
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• 2019

We introduce anti-invariant Riemannian submersions from almost paracontact Riemannian manifolds onto Riemannian manifolds. We give an example, investigate the geometry of foliations which are arisen from the definition of a Riemannian submersion and check the harmonicity of such submersions.

• 대한수학회논문집
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• 제18권3호
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• pp.481-484
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• 2003

We will show that if U is a Bergman ball E($\alpha;\;\delta$) in $B_n\;\subset\;{\mathbb{C}_n}$ and if U has M-harmonic volume mean value property at a for all M-harmonic functions f on $\={U} $, then U must be a ball centered at the origin with $\alpha\;=\;0$.

• 대한수학회논문집
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• 제35권3호
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• pp.1019-1035
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• 2020

In this paper, we introduce the deformed-Sasaki metric on the tangent bundle TM over an m-dimensional Riemannian manifold (M, g), as a new natural metric on TM. We establish a necessary and sufficient conditions under which a vector field is harmonic with respect to the deformed-Sasaki Metric. We also construct some examples of harmonic vector fields.