𝐡-principles for hypersurfaces with prescribed principle curvatures and directions

DOI10.1090/S0002-9947-06-04092-XzbMath1099.53005MaRDI QIDQ5473445

Mohammad Ghomi, Marek Kossowski

Publication date: 21 June 2006

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

hypersurfaceGauss curvatureprincipal curvature\(h\)-principleprincipal directionregular homotopyholonomic approximation

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) Partial differential equations on manifolds; differential operators (58J99) Immersions in differential topology (57R42)

Related Items (6)

NEGATIVELY CURVED MÖBIUS STRIPS ON GIVEN KNOTS ⋮ \(h\)-principles for curves and knots of constant curvature ⋮ Directed immersions of closed manifolds ⋮ Topology of Riemannian submanifolds with prescribed boundary ⋮ A Riemannian four vertex theorem for surfaces with boundary ⋮ Normal curvatures of asymptotically constant graphs and Carathéodory’s conjecture

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