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<p>In this paper, we consider the holomorphic map between complex manifolds satisfying certain partial differential equation which generalizes the holomorphic isometry and the holomorphic map preserving (<i>p</i>,&#xa0;<i>p</i>)-forms. On one hand, we study the non-existence of such maps between complex space forms of different types. On the other hand, the rigidity phenomena for such maps between complex space forms of the same type are also obtained.</p>

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Holomorphic Maps Between Complex Space Forms Satisfying Certain Partial Differential Equations

  • 期刊论文

  • 发表日期：

    2025年3月18日

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  • Xiaoliang Cheng,
  • Mingyue Chi,
  • Xu Zhang

摘要

In this paper, we consider the holomorphic map between complex manifolds satisfying certain partial differential equation which generalizes the holomorphic isometry and the holomorphic map preserving (p, p)-forms. On one hand, we study the non-existence of such maps between complex space forms of different types. On the other hand, the rigidity phenomena for such maps between complex space forms of the same type are also obtained.