On the structure of submanifolds in Euclidean space with flat normal bundle

DOI10.1007/s00025-015-0435-5zbMath1330.53079OpenAlexW2056327553MaRDI QIDQ889133

He-Zi Lin

Publication date: 6 November 2015

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00025-015-0435-5

zbMATH Keywords

submanifoldsBetti number\(L^2\)-harmonic \(p\)-formstotal curvature

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Characteristic classes and numbers in differential topology (57R20) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Related Items (12)

Vanishing properties of $p$-harmonic $\ell$-forms on Riemannian manifolds ⋮ Harmonic \(p\)-forms on Hadamard manifolds with finite total curvature ⋮ VANISHING THEOREMS FOR HYPERSURFACES IN THE UNIT SPHERE ⋮ Eigenvalue estimate and gap theorems for submanifolds in the hyperbolic space ⋮ Cohomology vanishing theorems for free boundary submanifolds ⋮ Vanishing theorems for the cohomology groups of free boundary submanifolds ⋮ \(p\)-harmonic \(l\)-forms on complete noncompact submanifolds in sphere with flat normal bundle ⋮ On the structure of submanifolds in the hyperbolic space ⋮ \(p\)-harmonic \(\ell\)-forms on Riemannian manifolds with a weighted Poincaré inequality ⋮ The \(p\)-eigenvalue estimates and \(L^q\)\( p\)-harmonic forms on submanifolds of Hadamard manifolds ⋮ Analysis of weighted p-harmonic forms and applications ⋮ Homology vanishing theorems for pinched submanifolds

Cites Work

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• \(L^2\)-harmonic 1-forms on submanifolds with finite total curvature
• Total curvature and \(L ^{2}\) harmonic 1-forms on complete submanifolds in space forms
• Harmonic maps and the topology of stable hypersurfaces and manifolds with non-negative Ricci curvature
• The structure of stable minimal hypersurfaces in \(\mathbb{R}^{n+1}\)
• Refined Kato inequalities and conformal weights in Riemannian geometry
• Total scalar curvature and \(L^2\) harmonic 1-forms on a minimal hypersurface in Euclidean space
• Minimal hypersurfaces with finite index
• On the Sobolev constant and the $p$-spectrum of a compact riemannian manifold
• An Estimate on the Ricci Curvature of a Submanifold and Some Applications
• Sobolev and isoperimetric inequalities for riemannian submanifolds

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