Harmonic vector fields and the Hodge Laplacian operator on Finsler geometry
نویسندگان
چکیده
We first present the natural definitions of horizontal differential, divergence (as an adjoint operator), and a $p$-harmonic form on Finsler manifold. Next, we prove Hodge-type theorem for manifold in sense that $p$-form is harmonic if only Laplacian vanishes. This viewpoint provides new appropriate definition vector fields geometry. approach leads to Bochner-Yano type classification based Ricci scalar. Finally, show closed orientable with positive scalar has zero Betti number.
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ژورنال
عنوان ژورنال: Comptes Rendus Mathematique
سال: 2022
ISSN: ['1631-073X', '1778-3569']
DOI: https://doi.org/10.5802/crmath.287