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<p>In this paper, we define the H-energy for maps between Finsler tangent bundles, based on the potential sub-Riemannian structures on the tangent bundles of Finsler manifolds. We introduce a new connection on the Finsler tangent bundle, called HV-connection. Utilizing this connection, we study horizontal harmonic maps between Finsler manifolds, which are critical points under horizontal variations of the H-energy. Under certain additional assumptions, we establish an existence result (Theorem <InternalRef RefID="FPar29">6.6</InternalRef>) of the Dirichlet problem of horizontal harmonic map from compact Finsler manifolds with boundary.</p>

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Horizontal harmonic maps between finsler manifolds

  • 期刊论文

  • 发表日期：

    2025年10月11日

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  • Qun Chen,
  • Haowei Lin

摘要

In this paper, we define the H-energy for maps between Finsler tangent bundles, based on the potential sub-Riemannian structures on the tangent bundles of Finsler manifolds. We introduce a new connection on the Finsler tangent bundle, called HV-connection. Utilizing this connection, we study horizontal harmonic maps between Finsler manifolds, which are critical points under horizontal variations of the H-energy. Under certain additional assumptions, we establish an existence result (Theorem 6.6) of the Dirichlet problem of horizontal harmonic map from compact Finsler manifolds with boundary.