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<p>We derive an explicit formula for the Laplace–Beltrami operator on the orthogonal Stiefel manifold, viewed as a constraint submanifold of the Euclidean space of real matrices equipped with the Frobenius metric. Using the general framework of Laplace operators on constraint manifolds, we provide the formula for the Laplace–Beltrami operator in terms of the ambient Euclidean coordinates. The result extends previously known cases, recovering the formulas for the sphere and the special orthogonal group as particular instances.</p>

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An explicit formula for the Laplace–Beltrami operator on the Stiefel manifold

  • 期刊论文

  • 发表日期：

    2026年7月11日

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  • Petre Birtea,
  • Ioan Caşu,
  • Dan Comănescu

摘要

We derive an explicit formula for the Laplace–Beltrami operator on the orthogonal Stiefel manifold, viewed as a constraint submanifold of the Euclidean space of real matrices equipped with the Frobenius metric. Using the general framework of Laplace operators on constraint manifolds, we provide the formula for the Laplace–Beltrami operator in terms of the ambient Euclidean coordinates. The result extends previously known cases, recovering the formulas for the sphere and the special orthogonal group as particular instances.