On the Number of Distinct Isometric Immersions of a Riemannian Surface Into R 3 with Given Mean Curvature

DOI10.2307/2374853zbMATH Open0698.53001OpenAlexW2327565804WikidataQ115228791 ScholiaQ115228791MaRDI QIDQ3475932

Gaston E. Hernandez, Ioannis M. Roussos

Publication date: 1990

Published in: American Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2374853

zbMATH Keywords

surface of revolutionprescribed mean curvatureumbilical pointsnoncongruent isometric immersions

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Surfaces in Euclidean and related spaces (53A05)

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The problem of nontrivial isometries of surfaces preserving principal curvatures ⋮ An intrinsic characterization of Bonnet surfaces based on a closed differential ideal ⋮ Bonnet and isotropically isothermic surfaces in 4-dimensional space forms ⋮ On the moduli space of isometric surfaces with the same mean curvature in 4-dimensional space forms ⋮ Compact surfaces with no Bonnet mate ⋮ Isometric immersions of tori into \(\mathbb{R}^ 3\) with given mean curvature ⋮ Lagrangian Bonnet Problems in complex space forms ⋮ TWO CLASSES OF SPACELIKE STATIONARY SURFACES IN SEMI-RIEMANNIAN SPACE FORMS ⋮ On isometric immersions of a torus into a space form with the same mean curvature function ⋮ Tangential developable surfaces as Bonnet surfaces ⋮ Global results on Bonnet surfaces

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