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<p>In this paper, we introduce almost (<i>a</i>,&#xa0;<i>c</i>)-weighted Ricci solitons with weighted constants <i>a</i>,&#xa0;<i>c</i> in Finsler geometry, which include (gradient) almost Ricci solitons, (gradient) Ricci solitons, (<i>a</i>,&#xa0;<i>c</i>)-weighted Einstein Finsler metrics and Einstein Finsler metrics as special cases. In particular, we focus on a class of almost weighted Ricci solitons, called Kropina almost (<i>a</i>,&#xa0;<i>c</i>)-weighted Ricci solitons. We give two different types of equivalent characterizations for this class of solitons and their applications. Further, we classify Kropina almost Ricci solitons via the navigation data (<i>h</i>,&#xa0;<i>W</i>) of <i>F</i>. Based on this, we construct two examples of nontrivial Kropina Ricci solitons.</p>

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On a Class of Almost Weighted Ricci Solitons

  • 期刊论文

  • 发表日期：

    2025年2月15日

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  • Luyao Tan,
  • Qiaoling Xia

摘要

In this paper, we introduce almost (a, c)-weighted Ricci solitons with weighted constants a, c in Finsler geometry, which include (gradient) almost Ricci solitons, (gradient) Ricci solitons, (a, c)-weighted Einstein Finsler metrics and Einstein Finsler metrics as special cases. In particular, we focus on a class of almost weighted Ricci solitons, called Kropina almost (a, c)-weighted Ricci solitons. We give two different types of equivalent characterizations for this class of solitons and their applications. Further, we classify Kropina almost Ricci solitons via the navigation data (h, W) of F. Based on this, we construct two examples of nontrivial Kropina Ricci solitons.