• 대한수학회보
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• 제53권2호
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• pp.531-540
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• 2016

In this work, we introduce the complete Riemannian manifold $\mathbb{F}_3$ which is a three-dimensional real vector space endowed with a conformally flat metric that is a solution of the Einstein equation. We obtain a second order nonlinear ordinary differential equation that characterizes the helicoidal minimal surfaces in $\mathbb{F}_3$. We show that the helicoid is a complete minimal surface in $\mathbb{F}_3$. Moreover we obtain a local solution of this differential equation which is a two-parameter family of functions ${\lambda}_h,K_2$ explicitly given by an integral and defined on an open interval. Consequently, we show that the helicoidal motion applied on the curve defined from ${\lambda}_h,K_2$ gives a two-parameter family of helicoidal minimal surfaces in $\mathbb{F}_3$.

• 대한수학회논문집
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• 제38권1호
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• pp.205-221
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• 2023

The main goal of the paper is the introduction of the notion of conformal hemi-slant submersions from almost contact metric manifolds onto Riemannian manifolds. It is a generalization of conformal anti-invariant submersions, conformal semi-invariant submersions and conformal slant submersions. Our main focus is conformal hemi-slant submersion from cosymplectic manifolds. We tend also study the integrability of the distributions involved in the definition of the submersions and the geometry of their leaves. Moreover, we get necessary and sufficient conditions for these submersions to be totally geodesic, and provide some representative examples of conformal hemi-slant submersions.