Distance functions and umbilic submanifolds of hyperbolic space

DOI10.1017/S0027763000018444zbMath0401.53016OpenAlexW1565800914MaRDI QIDQ4185443

Patrick J. Ryan, Thomas E. Cecil

Publication date: 1979

Published in: Nagoya Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0027763000018444

zbMATH Keywords

Hyperbolic SpaceCritical Point TheoryUmbilic Submanifolds

Mathematics Subject Classification ID

Global submanifolds (53C40) Global Riemannian geometry, including pinching (53C20) Non-Euclidean differential geometry (53A35) Critical points and critical submanifolds in differential topology (57R70)

Related Items (7)

Tautness and Lie sphere geometry ⋮ Legendrian dual surfaces in hyperbolic 3-space ⋮ The horospherical Gauss-Bonnet type theorem in hyperbolic space ⋮ Folding maps on spacelike and timelike surfaces and duality ⋮ On the topology of closed manifolds with quasi-constant sectional curvature ⋮ Horo-tight spheres in hyperbolic space ⋮ Horospherical flat surfaces in hyperbolic 3-space

Cites Work

• A characterization of metric spheres in hyperbolic space by Morse theory
• Geometric applications of critical point theory to submanifolds of complex projective space
• Umbilical Submanifolds and Morse Functions

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