Nonexistence of nontrivial ๐๐โ-harmonic 1-forms on a complete foliated Riemannian manifold
Nonexistence of nontrivial ๐๐โ-harmonic 1-forms on a complete foliated Riemannian manifold
We study the nonexistence of nontrivial <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="white medium square"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>โป</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">\square</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-harmonic 1-forms on a complete foliated riemannian manifold with positive definite Ricci curvature. It is well known that the harmonic 1-form on a compact and orientable riemannian manifold โฆ