Vanishing theorems for \(L^2\) harmonic forms on complete submanifolds in Euclidean space

DOI10.1016/J.JMAA.2014.12.065zbMath1307.53005OpenAlexW2076278924MaRDI QIDQ2512672

He-Zi Lin

Publication date: 30 January 2015

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2014.12.065

zbMATH Keywords

second fundamental formsubmanifoldmean curvatureWeitzenböck formulaendsvanishing theorem\(L^2\)-harmonic \(p\)-formstotal curvature

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (10)

Geometries and topologies of conformally flat Riemannian manifolds ⋮ Harmonic \(p\)-forms on Hadamard manifolds with finite total curvature ⋮ VANISHING THEOREMS FOR HYPERSURFACES IN THE UNIT SPHERE ⋮ \(L^{p}\) harmonic 1-forms on submanifolds in spheres ⋮ Eigenvalue estimate and gap theorems for submanifolds in the hyperbolic space ⋮ Vanishing theorem for \(p\)-harmonic 1-forms on complete submanifolds in spheres ⋮ \(p\)-harmonic \(l\)-forms on complete noncompact submanifolds in sphere with flat normal bundle ⋮ On the structure of submanifolds in the hyperbolic space ⋮ Rigidity and vanishing theorems for submanifolds with free boundary in the unit ball ⋮ The \(p\)-eigenvalue estimates and \(L^q\)\( p\)-harmonic forms on submanifolds of Hadamard manifolds

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