Submanifolds in Euclidean space with simple geodesics

DOI10.1007/BF01475754zbMath0474.53004OpenAlexW2077550897MaRDI QIDQ1158842

Stephan Schirrmacher, Dirk Ferus

Publication date: 1982

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/163655

zbMATH Keywords

geodesicsFrenet curvaturesextrinsic symmetricW-curve

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Curves in Euclidean and related spaces (53A04)

Related Items (9)

Totally geodesic immersions of Kähler manifolds and Kähler Frenet curves ⋮ Families of congruent curves and applications ⋮ On some properties which characterize symmetric and general \(R\)-spaces ⋮ CHARACTERISATIONS OF GEODESIC HYPERSPHERES IN A NON-FLAT COMPLEX SPACE FORM ⋮ Extrinsic geodesics and hypersurfaces of type (A) in a complex projective space ⋮ Homogeneous totally real submanifolds of complex projective space ⋮ Holomorphic helices in a complex space form ⋮ Helical immersions and normal sections ⋮ Surfaces of a Euclidean space with helical or planar geodesics through a point

Cites Work

• Symmetric submanifolds of Riemannian manifolds
• Symmetric submanifolds of Euclidean space
• On a certain minimal immersion of a Riemannian manifold into a sphere
• Helical immersions into a unit sphere
• Manifolds with planar geodesics
• Planar geodesic immersions
• Planar geodesic submanifolds in complex space forms
• Isometric immersions of manifolds with plane geodesics into Euclidean space
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