Local isometric embedding problem of Riemannian 3-manifold into \(R^ 6\)

DOI10.3792/PJAA.62.257zbMath0622.53015OpenAlexW2030698194WikidataQ115219949 ScholiaQ115219949MaRDI QIDQ1090943

Gen Nakamura, Yoshiaki Maeda

Publication date: 1986

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3792/pjaa.62.257

zbMATH Keywords

isometric embeddingimplicit function theoremgeometric applications of functional analysis

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Local submanifolds (53B25)

Related Items (6)

Existence of $C^\{\infty \}$ local solutions of the complex Monge-Ampère equation ⋮ Lectures on the Isometric Embedding Problem $$(M^{n},g)\rightarrow \mathrm {I\!R\!}^{m},\,m=\frac{n}{2}(n+1)$$ ⋮ Isometric immersions of surfaces with two classes of metrics and negative Gauss curvature ⋮ Global weak rigidity of the Gauss-Codazzi-Ricci equations and isometric immersions of Riemannian manifolds with lower regularity ⋮ Weak continuity of the Gauss-Codazzi-Ricci system for isometric embedding ⋮ Fluids, geometry, and the onset of Navier-Stokes turbulence in three space dimensions

Cites Work

• Characteristics and existence of isometric embeddings
• Fourier integral operators. II
• The local isometric embedding inR3 of two-dimensional riemannian manifolds with gaussian curvature changing sign cleanly

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