Geometric properties for Gaussian image of submanifolds in \(S^{n+p} (1)\)

DOI10.1007/s11766-007-0315-1zbMath1150.53020OpenAlexW1990079045MaRDI QIDQ933044

Wei Zhang, Hong-Wei Xu

Publication date: 6 August 2008

Published in: Applied Mathematics. Series B (English Edition) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11766-007-0315-1

zbMATH Keywords

second fundamental formsubmanifoldmean curvatureGaussian image

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global submanifolds (53C40)

Cites Work

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• On the total curvature of immersed manifolds. II
• Curvature, diameter and Betti numbers
• Lower bound for \(L^{n/2}\) curvature norm and its application
• Geometric finiteness theorems via controlled topology
• On the topology, volume, diameter and Gauss map image of submanifolds in a sphere
• The Gauss map of immersions of Riemannian manifolds in spaces of constant curvature
• Cheeger's finiteness theorem for diffeomorphism classes of Riemannian manifolds.
• The geometry of the generalized Gauss map
• The Harmonic Gauss Maps in a Generalized Sense

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