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Difference between revisions of "Virtually-asymptotic net"

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A [[Net (in differential geometry)|net (in differential geometry)]] on a surface <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/v/v096/v096750/v0967501.png" /> in Euclidean space which, on being deformed somewhat (<img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/v/v096/v096750/v0967502.png" />), becomes an [[Asymptotic net|asymptotic net]] of the surface <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/v/v096/v096750/v0967503.png" />. A [[Voss surface|Voss surface]] is distinguished by the presence of a conjugate virtually-asymptotic net.
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A [[Net (in differential geometry)|net (in differential geometry)]] on a surface $  V _ {2} $
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in Euclidean space which, on being deformed somewhat ( $  f: V _ {2} \rightarrow V _ {2}  ^ {*} $),  
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becomes an [[Asymptotic net|asymptotic net]] of the surface $  V _ {2}  ^ {*} $.  
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A [[Voss surface|Voss surface]] is distinguished by the presence of a conjugate virtually-asymptotic net.
  
 
====References====
 
====References====
 
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  V.I. Shulikovskii,  "Classical differential geometry in a tensor setting" , Moscow  (1963)  (In Russian)</TD></TR></table>
 
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  V.I. Shulikovskii,  "Classical differential geometry in a tensor setting" , Moscow  (1963)  (In Russian)</TD></TR></table>

Latest revision as of 08:28, 6 June 2020


A net (in differential geometry) on a surface $ V _ {2} $ in Euclidean space which, on being deformed somewhat ( $ f: V _ {2} \rightarrow V _ {2} ^ {*} $), becomes an asymptotic net of the surface $ V _ {2} ^ {*} $. A Voss surface is distinguished by the presence of a conjugate virtually-asymptotic net.

References

[1] V.I. Shulikovskii, "Classical differential geometry in a tensor setting" , Moscow (1963) (In Russian)
How to Cite This Entry:
Virtually-asymptotic net. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Virtually-asymptotic_net&oldid=49152
This article was adapted from an original article by V.T. Bazylev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article