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<p>In this article, we study the rigidity theorems of strongly harmonic maps from Kähler-Finsler manifolds to Kähler and Riemannian manifolds, respectively. Firstly, we prove that a strongly harmonic map <i>f</i> from a compact connected Kähler-Finsler manifold to a compact Kähler manifold is either holomorphic or anti-holomorphic if the curvature tensor of the target manifold is very strongly negative and <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\textrm{rank}_{\textbf{R}}df \ge 3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mtext>rank</mtext> <mi mathvariant="bold">R</mi> </msub> <mi>d</mi> <mi>f</mi> <mo>≥</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation> at some point. Secondly, we show that a strongly harmonic map from a compact Kähler-Finsler manifold to a compact Riemannian manifold is necessarily totally geodesic if the target manifold has very Hermitian negative curvature and the source manifold possesses semi-positive definite Ricci curvature tensors associated to the complex Rund connection. Finally, we examine the pluriharmonicity of strongly harmonic maps from a non-compact Kähler-Finsler manifold under the assumption of finite <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\partial \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>∂</mi> </math></EquationSource> </InlineEquation>-energy or <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\({\bar{\partial }}\)</EquationSource> <EquationSource Format="MATHML"><math> <mover accent="true"> <mrow> <mi>∂</mi> </mrow> <mrow> <mo stretchy="false">¯</mo> </mrow> </mover> </math></EquationSource> </InlineEquation>-energy functionals.</p>

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Rigidity Theorems of Strongly Harmonic Maps from Kähler-Finsler Manifolds

  • 期刊论文

  • 发表日期：

    2025年12月22日

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  • Hongjun Li,
  • Jintang Li,
  • Chunhui Qiu,
  • Chang Tian

摘要

In this article, we study the rigidity theorems of strongly harmonic maps from Kähler-Finsler manifolds to Kähler and Riemannian manifolds, respectively. Firstly, we prove that a strongly harmonic map f from a compact connected Kähler-Finsler manifold to a compact Kähler manifold is either holomorphic or anti-holomorphic if the curvature tensor of the target manifold is very strongly negative and \(\textrm{rank}_{\textbf{R}}df \ge 3\) rank R d f ≥ 3 at some point. Secondly, we show that a strongly harmonic map from a compact Kähler-Finsler manifold to a compact Riemannian manifold is necessarily totally geodesic if the target manifold has very Hermitian negative curvature and the source manifold possesses semi-positive definite Ricci curvature tensors associated to the complex Rund connection. Finally, we examine the pluriharmonicity of strongly harmonic maps from a non-compact Kähler-Finsler manifold under the assumption of finite \(\partial \) ∂ -energy or \({\bar{\partial }}\) ∂ ¯ -energy functionals.