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It is well known that a unit sphere admits Sasakian 3-structure. Also, Sasakian manifolds are locally isometric to a unit sphere under several curvature and critical conditions. So, a natural question is: Does there exist any curvature or critical condition under which a Sasakian 3-manifold represents a geometrical object other than the unit sphere? In this regard, as an extension of the $\ast$-Ricci soliton, the notion of $\ast$-Ricci-Yamabe soliton is introduced and studied on two classes contact metric manifolds. A $(2n + 1)$-dimensional non-Sasakian $N(k)$-contact metric manifold admitting $\ast$-Ricci-Yamabe soliton is completely classified. Further, it is proved that if a Sasakian 3-manifold $M$ admits $\ast$-Ricci-Yamabe soliton $(g,V,\lambda,\alpha,\beta)$ under certain conditions on the soliton vector field $V$, then $M$ is $\ast$-Ricci flat, positive Sasakian and the transverse geometry of $M$ is Fano. In addition, the Sasakian 3-metric $g$ is homothetic to a Berger sphere and the soliton is steady. Also, the potential vector field $V$ is an infinitesimal automorphism of the contact metric structure.

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기사명 저자명 페이지 원문 목차
∗-Ricci-Yamabe soliton and contact geometry Dibakar Dey p. 303-315
Solution and stability of a functional equation deriving from additive, quadratic and quartic in quasi-Banach spaces Norouz Ghobadipour, Mohammad Golestani, Choonkil Park p. 317-342
Existence and uniqueness of positive solutions for a class of fractional differential equations with a parameter Pengcheng Yuan, Zhaocai Hao, Martin Bohner p. 343-354
On zero-dimensional spaces of closed subsets Namjip Koo, Hyunhee Lee p. 355-362
Inducing the sum of the Fibonacci sequences from the moment of inertia of an object Woojun Lee, Dohyun Lee, Juha Oh, Jinseo Park p. 363-368
(A) reexamination of semigroup homomorphisms arising from the product structure in pure quartic number fields Pratchaya Singjanusong, Wutiphol Sintunavarat p. 369-379
Affine relations in the card game SET and related games Hanchul Park p. 381-388
Functional inequalities and pairs of hom-derivations and homomorphisms Se Won Min, Choonkil Park p. 389-399

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