Orthogonal asymptotic lines on surfaces immersed in \(\mathbb{R}^4\)

DOI10.1216/RMJ-2009-39-5-1597zbMath1178.53006arXivmath/0606245MaRDI QIDQ734584

Luis Fernando Mello

Publication date: 13 October 2009

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0606245

zbMATH Keywords

normal curvaturehypersphericityAsymptotic linesinflections points

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Global submanifolds (53C40)

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Cites Work

• Unnamed Item
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• Immersions of surfaces into 4-dimensional spaces with nonzero normal curvature
• A note on some developments on Carathéodory conjecture on umbilic points
• Lines of axial curvature on surfaces immersed in \(\mathbb{R}^4\)
• Umbilicity of surfaces with orthogonal asymptotic lines in \(\mathbb R^ 4\).
• A differential equation for lines of curvature on surfaces immersed in \(\mathbb{R}^4\)
• Closed principal lines of surfaces immersed in the Euclidean 4-space
• Mean directionally curved lines on surfaces immersed in \(\mathbb{R}^4\)
• Lines of curvature near umbilical points on surfaces immersed in \(\mathbb{R}^ 4\)
• The geometry of surfaces in 4-space from a contact viewpoint
• On a Loewner umbilic-index conjecture for surfaces immersed in \({\mathbb{R}}^4\)
• On singularities of submanifolds of higher dimensional Euclidean spaces
• A new curvature theory for surfaces in a Euclidean \(4\)-space
• Lines of curvature on surfaces immersed in ?4
• Inflection points and topology of surfaces in 4-space