エンネパー曲面
a = − ( u 2 − v 2 ) ( 1 + u 2 / 3 + v 2 / 3 ) , {\displaystyle a=-(u^{2}-v^{2})(1+u^{2}/3+v^{2}/3),\ }
b = 6 u , {\displaystyle b=6u,\ }
c = 6 v , {\displaystyle c=6v,\ }
d = − 3 ( 1 − u 2 − v 2 ) {\displaystyle d=-3(1-u^{2}-v^{2})}
と書ける。この係数は次の6次多項式を満たす。
162 a 2 b 2 c 2 + 6 b 2 c 2 d 2 − 4 ( b 6 + c 6 ) + 54 ( a b 4 d − a c 4 d ) + 81 ( a 2 b 4 + a 2 c 4 ) {\displaystyle 162a^{2}b^{2}c^{2}+6b^{2}c^{2}d^{2}-4(b^{6}+c^{6})+54(ab^{4}d-ac^{4}d)+81(a^{2}b^{4}+a^{2}c^{4})\ }
+ 4 ( b 4 c 2 + b 2 c 4 ) − 3 ( b 4 d 2 + c 4 d 2 ) + 36 ( a b 2 d 3 − a c 2 d 3 ) = 0 {\displaystyle {}+4(b^{4}c^{2}+b^{2}c^{4})-3(b^{4}d^{2}+c^{4}d^{2})+36(ab^{2}d^{3}-ac^{2}d^{3})=0}
ヤコビ行列式、ガウス曲率、平均曲率(英語版)はそれぞれ