Equiareal

Let $M,N$ be surfaces in the Euclidean space $mathbb{R}^3$ . A smooth map $f:M
ightarrow N$ is called equiareal if

: $|df_p(v) imes df_p(w)|=|v imes w|,$

for all $pin M$ and $v,win T_pM$ , where the latter denotes the tangent space to $M.$

For some examples of such maps see map projection.For the case "M" = "N" = R x R, see equi-areal mapping.

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