Embedded Surface
A surface S is n-embeddable if it can be placed in R^n-space without self-intersections, but cannot be similarly placed in any R^k for k<n. A surface so embedded is said to be an embedded surface. The Costa minimal surface and gyroid are embeddable in R^3, but the Klein bottle is not (the commonly depicted R^3 representation requires the surface to pass through itself).
There is particular interest in surfaces which are minimal, complete, and embedded.
See also
Costa Minimal Surface, Embeddable Knot, Gyroid, Minimal SurfaceExplore with Wolfram|Alpha
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References
Collin, P. "Topologie et courbure des surfaces minimales proprement plongées de R^3." Ann. Math. 145, 1-31, 1997.Hoffman, D. and Karcher, H. "Complete Embedded Minimal Surfaces of Finite Total Curvature." In Minimal Surfaces (Ed. R. Osserman). Berlin: Springer-Verlag, pp. 267-272, 1997.Nikolaos, K. "Complete Embedded Minimal Surfaces of Finite Total Curvature." J. Diff. Geom. 47, 96-169, 1997.Pérez, J. and Ros, A. "The Space of Properly Embedded Minimal Surfaces with Finite Total Curvature." Indiana Univ. Math. J. 45, 177-204, 1996.Ros, A. "Compactness of Spaces of Properly Embedded Minimal Surfaces with Finite Total Curvature." Indiana Univ. Math. J. 44, 139-152, 1995.Referenced on Wolfram|Alpha
Embedded SurfaceCite this as:
Weisstein, Eric W. "Embedded Surface." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/EmbeddedSurface.html