• 대한수학회논문집
• /
• 제39권1호
• /
• pp.161-173
• /
• 2024

The main object of the present paper is to study conformal Ricci soliton on paracontact metric (k, 𝜇)-manifolds with respect to Schouten-van Kampen connection. Further, we obtain the result when paracontact metric (k, 𝜇)-manifolds with respect to Schouten-van Kampen connection satisfying the condition $^*_C({\xi},U){\cdot}^*_S=0$. Finally we characterized concircular curvature tensor on paracontact metric (k, 𝜇)-manifolds with respect to Schouten-van Kampen connection.

• Kyungpook Mathematical Journal
• /
• 제63권4호
• /
• pp.623-638
• /
• 2023

In this article we study a 𝛿-Ricci-Yamabe almost soliton within the framework of paracontact metric manifolds. In particular we study 𝛿-Ricci-Yamabe almost soliton and gradient 𝛿-Ricci-Yamabe almost soliton on K-paracontact and para-Sasakian manifolds. We prove that if a K-paracontact metric g represents a 𝛿-Ricci-Yamabe almost soliton with the non-zero potential vector field V parallel to 𝜉, then g is Einstein with Einstein constant -2n. We also show that there are no para-Sasakian manifolds that admit a gradient 𝛿-Ricci-Yamabe almost soliton. We demonstrate a 𝛿-Ricci-Yamabe almost soliton on a (𝜅, 𝜇)-paracontact manifold.

• 호남수학학술지
• /
• 제37권4호
• /
• pp.457-468
• /
• 2015

The aim of present paper is to investigate 3-dimensional ${\xi}$-projectively flt and $\tilde{\varphi}$-projectively flt normal almost paracontact metric manifolds. As a first step, we proved that if the 3-dimensional normal almost paracontact metric manifold is ${\xi}$-projectively flt then ${\Delta}{\beta}=0$. If additionally ${\beta}$ is constant then the manifold is ${\beta}$-para-Sasakian. Later, we proved that a 3-dimensional normal almost paracontact metric manifold is $\tilde{\varphi}$-projectively flt if and only if it is an Einstein manifold for ${\alpha},{\beta}=const$. Finally, we constructed an example to illustrate the results obtained in previous sections.

• Korean Journal of Mathematics
• /
• 제28권3호
• /
• pp.555-571
• /
• 2020

The aim of the present paper is to study pseudoparallel invariant submanifold of a (𝜅, 𝜇)-paracontact metric manifold. We consider pseudoparallel, Ricci-generalized pseudoparallel and 2-Ricci generalized pseudo parallel invariant submanifolds of a (𝜅, 𝜇)-paracontact metric manifold and we obtain new results contribute to geometry.

• 호남수학학술지
• /
• 제43권1호
• /
• pp.35-46
• /
• 2021

The purpose of this paper is to study invariant pseudoparallel, Ricci generalized pseudoparallel and 2-Ricci generalized pseudoparallel submanifold of a para-Kenmotsu manifold and I obtained some equivalent conditions of invariant submanifolds of para-Kenmotsu manifolds under some conditions which the submanifolds are totally geodesic. Finally, a non-trivial example of invariant submanifold of paracontact metric manifold is constructed in order to illustrate our results.