• 제목/요약/키워드: Ricci curvature

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TIME ANALYTICITY FOR THE HEAT EQUATION UNDER BAKRY-ÉMERY RICCI CURVATURE CONDITION

  • Ling Wu
    • 대한수학회보
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    • 제60권6호
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    • pp.1673-1685
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    • 2023
  • Inspired by Hongjie Dong and Qi S. Zhang's article [3], we find that the analyticity in time for a smooth solution of the heat equation with exponential quadratic growth in the space variable can be extended to any complete noncompact Riemannian manifolds with Bakry-Émery Ricci curvature bounded below and the potential function being of at most quadratic growth. Therefore, our result holds on all gradient Ricci solitons. As a corollary, we give a necessary and sufficient condition on the solvability of the backward heat equation in a class of functions with the similar growth condition. In addition, we also consider the solution in certain Lp spaces with p ∈ [2, +∞) and prove its analyticity with respect to time.

MANIFOLDS WITH NONNEGATIVE RICCI CURVATURE ALMOST EVERYWHERE

  • Paeng, Seong-Hun
    • 대한수학회지
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    • 제36권1호
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    • pp.125-137
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    • 1999
  • Under the condition of RicM $\geq$ -(n-1), injM $\geq$ I0, we prove the existence of an $\varepsilon$>0 such that on the region of volume $\varepsilon$>0 the curvature condition of splitting theorem can be weakened.

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NEW VOLUME COMPARISON WITH ALMOST RICCI SOLITON

  • azami, Shahroud;Hajiaghasi, Sakineh
    • 대한수학회논문집
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    • 제37권3호
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    • pp.839-849
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    • 2022
  • In this paper we consider a condition on the Ricci curvature involving vector fields which enabled us to achieve new results for volume comparison and Laplacian comparison. These results in special case obtained with considering volume non-collapsing condition. Also, by applying this condition we get new results of volume comparison for almost Ricci solitons.

𝜂-RICCI SOLITONS ON PARA-KENMOTSU MANIFOLDS WITH SOME CURVATURE CONDITIONS

  • Mondal, Ashis
    • Korean Journal of Mathematics
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    • 제29권4호
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    • pp.705-714
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    • 2021
  • In the present paper, we study 𝜂-Ricci solitons on para-Kenmotsu manifolds with Codazzi type of the Ricci tensor. We study 𝜂-Ricci solitons on para-Kenmotsu manifolds with cyclic parallel Ricci tensor. We also study 𝜂-Ricci solitons on 𝜑-conformally semi-symmetric, 𝜑-Ricci symmetric and conformally Ricci semi-symmetric para-Kenmotsu manifolds. Finally, we construct an example of a three-dimensional para-Kenmotsu manifold which admits 𝜂-Ricci solitons.

ON LIGHTLIKE SUBMANIFOLDS OF A GRW SPACE-TIME

  • Kang, Tae Ho
    • 대한수학회논문집
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    • 제29권2호
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    • pp.295-310
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    • 2014
  • This paper provides a study of lightlike submanifolds of a generalized Robertson-Walker (GRW) space-time. In particular, we investigate lightlike submanifolds with curvature invariance, parallel second fundamental forms, totally umbilical second fundamental forms, null sectional curvatures and null Ricci curvatures, respectively.