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Difference between revisions of "Enneper surface"

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An algebraic [[Minimal surface|minimal surface]] covering a surface of revolution. Its parametric equation is
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<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/e/e035/e035710/e0357102.png" /></td> </tr></table>
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An algebraic [[Minimal surface|minimal surface]] covering a [[surface of revolution]]. Its parametric equation is
  
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<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/e/e035/e035710/e0357103.png" /></td> </tr></table>
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$$
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x  =
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\frac{1}{4}
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( u  ^ {3} - 3 u - 3 u v  ^ {2} ) ,
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$$
  
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It was discovered by A. Enneper in 1864.
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$$
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y  = 
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\frac{1}{4}
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( 3 v + 3 u  ^ {2} v - v  ^ {3} ) ,
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$$
  
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$$
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z  = 
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\frac{3}{4}
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( v  ^ {2} - u  ^ {2} ) .
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$$
  
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It was discovered by A. Enneper in 1864.
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====Comments====
 
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====References====
 
====References====
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<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  J.C.C. Nitsche,   "Vorlesungen über Minimalflächen" , Springer (1975)</TD></TR></table>
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* {{Ref|a1}} J.C.C. Nitsche, "Vorlesungen über Minimalflächen", Springer (1975) {{ZBL|0319.53003}}

Latest revision as of 18:19, 28 March 2023


An algebraic minimal surface covering a surface of revolution. Its parametric equation is

$$ x = \frac{1}{4} ( u ^ {3} - 3 u - 3 u v ^ {2} ) , $$

$$ y = \frac{1}{4} ( 3 v + 3 u ^ {2} v - v ^ {3} ) , $$

$$ z = \frac{3}{4} ( v ^ {2} - u ^ {2} ) . $$

It was discovered by A. Enneper in 1864.

References

  • [a1] J.C.C. Nitsche, "Vorlesungen über Minimalflächen", Springer (1975) Zbl 0319.53003
How to Cite This Entry:
Enneper surface. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Enneper_surface&oldid=15167
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article
Retrieved from "https://encyclopediaofmath.org/index.php?title=Enneper_surface&oldid=53525"