• 제목/요약/키워드: Conformal

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CERTAIN SOLITONS ON GENERALIZED (𝜅, 𝜇) CONTACT METRIC MANIFOLDS

  • Sarkar, Avijit;Bhakta, Pradip
    • Korean Journal of Mathematics
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    • 제28권4호
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    • pp.847-863
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    • 2020

  • The aim of the present paper is to study some solitons on three dimensional generalized (𝜅, 𝜇)-contact metric manifolds. We study gradient Yamabe solitons on three dimensional generalized (𝜅, 𝜇)-contact metric manifolds. It is proved that if the metric of a three dimensional generalized (𝜅, 𝜇)-contact metric manifold is gradient Einstein soliton then ${\mu}={\frac{2{\kappa}}{{\kappa}-2}}$. It is shown that if the metric of a three dimensional generalized (𝜅, 𝜇)-contact metric manifold is closed m-quasi Einstein metric then ${\kappa}={\frac{\lambda}{m+2}}$ and 𝜇 = 0. We also study conformal gradient Ricci solitons on three dimensional generalized (𝜅, 𝜇)-contact metric manifolds.

  • https://doi.org/10.11568/kjm.2020.28.4.847 인용 PDF KSCI

STUDY OF P-CURVATURE TENSOR IN THE SPACE-TIME OF GENERAL RELATIVITY

  • Ganesh Prasad Pokhariyal;Sudhakar Kumar Chaubey
    • 호남수학학술지
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    • 제45권2호
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    • pp.316-324
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    • 2023

  • The P-curvature tensor has been studied in the space-time of general relativity and it is found that the contracted part of this tensor vanishes in the Einstein space. It is shown that Rainich conditions for the existence of non-null electro variance can be obtained by P𝛼𝛽. It is established that the divergence of tensor G𝛼𝛽 defined with the help of P𝛼𝛽 and scalar P is zero, so that it can be used to represent Einstein field equations. It is shown that for V4 satisfying Einstein like field equations, the tensor P𝛼𝛽 is conserved, if the energy momentum tensor is Codazzi type. The space-time satisfying Einstein's field equations with vanishing of P-curvature tensor have been considered and existence of Killing, conformal Killing vector fields and perfect fluid space-time has been established.

  • https://doi.org/10.5831/HMJ.2023.45.2.316 인용 PDF

A NOTE ON HARMONIC MAPPINGS

  • Hong, Suk Ho
    • Korean Journal of Mathematics
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    • 제4권1호
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    • pp.65-70
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    • 1996

  • In this note, we study a relation between harmonic maps and exponential harmonic maps, and we show existence of Yang-Mills connections.

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SOME GEOMETRIC APPLICATIONS OF EXTREMAL LENGTH (I)

  • Chung, Bo-Hyun
    • 충청수학회지
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    • 제12권1호
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    • pp.193-196
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    • 1999

  • In this note, we present some geometric applications of extremal length to analytic functions. We drive an interesting formula by the method of extremal length.

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