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RISS 인기검색어
- 검색키워드
- 저자 : Dhriti Sundar Patra (검색결과 4 건)
- 무료
- 기관 내 무료
- 유료
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Ricci solitons and Ricci almost solitons on para-Kenmotsu manifold
Dhriti Sundar Patra 대한수학회 2019 대한수학회보 Vol.56 No.5
The purpose of this article is to study the Ricci solitons and Ricci almost solitons on para-Kenmotsu manifold. First, we prove that if a para-Kenmotsu metric represents a Ricci soliton with the soliton vector field $V$ is contact, then it is Einstein and the soliton is shrinking. Next, we prove that if a $\eta$-Einstein para-Kenmotsu metric represents a Ricci soliton, then it is Einstein with constant scalar curvature and the soliton is shrinking. Further, we prove that if a para-Kenmotsu metric represents a gradient Ricci almost soliton, then it is $\eta$-Einstein. This result is also hold for Ricci almost soliton if the potential vector field $V$ is pointwise collinear with the Reeb vector field $\xi$.
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RICCI SOLITONS AND RICCI ALMOST SOLITONS ON PARA-KENMOTSU MANIFOLD
Patra, Dhriti Sundar Korean Mathematical Society 2019 대한수학회보 Vol.56 No.5
The purpose of this article is to study the Ricci solitons and Ricci almost solitons on para-Kenmotsu manifold. First, we prove that if a para-Kenmotsu metric represents a Ricci soliton with the soliton vector field V is contact, then it is Einstein and the soliton is shrinking. Next, we prove that if a ${\eta}$-Einstein para-Kenmotsu metric represents a Ricci soliton, then it is Einstein with constant scalar curvature and the soliton is shrinking. Further, we prove that if a para-Kenmotsu metric represents a gradient Ricci almost soliton, then it is ${\eta}$-Einstein. This result is also hold for Ricci almost soliton if the potential vector field V is pointwise collinear with the Reeb vector field ${\xi}$.
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The $k$-almost Ricci solitons and contact geometry
Amalendu Ghosh,Dhriti Sundar Patra 대한수학회 2018 대한수학회지 Vol.55 No.1
The aim of this article is to study the $k$-almost Ricci soliton and $k$-almost gradient Ricci soliton on contact metric manifold. First, we prove that if a compact $K$-contact metric is a $k$-almost gradient Ricci soliton, then it is isometric to a unit sphere $S^{2n+1}$. Next, we extend this result on a compact $k$-almost Ricci soliton when the flow vector field $X$ is contact. Finally, we study some special types of $k$-almost Ricci solitons where the potential vector field $X$ is point wise collinear with the Reeb vector field $\xi$ of the contact metric structure.
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THE k-ALMOST RICCI SOLITONS AND CONTACT GEOMETRY
Ghosh, Amalendu,Patra, Dhriti Sundar Korean Mathematical Society 2018 대한수학회지 Vol.55 No.1
The aim of this article is to study the k-almost Ricci soliton and k-almost gradient Ricci soliton on contact metric manifold. First, we prove that if a compact K-contact metric is a k-almost gradient Ricci soliton, then it is isometric to a unit sphere $S^{2n+1}$. Next, we extend this result on a compact k-almost Ricci soliton when the flow vector field X is contact. Finally, we study some special types of k-almost Ricci solitons where the potential vector field X is point wise collinear with the Reeb vector field ${\xi}$ of the contact metric structure.
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