Gauss map is holomorphic (as a map to the Riemann sphere) if the surface is minimal. This is Lemma 8.3 in the book of Osserman, a Survey of Riemann surfaces. In fact, if you replace "embedded" by "immersed" then the converse is also true (see Wikipedia article, https://en.wikipedia.org/wiki/Minimal_surface scroll down to "Gauss map definition".

Gauss map is holomorphic (as a map to the Riemann sphere) if the surface is minimal. This is Lemma 8.3 in the book of Osserman, A Survey of Minimal Surfaces. In fact, if you replace "embedded" by "immersed" then the converse is also true (see Wikipedia article, https://en.wikipedia.org/wiki/Minimal_surface scroll down to "Gauss map definition".

Gauss map is holomorphic (as a map to the Riemann sphere) if the surface is minimal. This is Lemma 8.3 in the book of Osserman, a Survey of Riemann surfaces. In fact, if you replace "embedded" by "immersed" then the converse is also true (see Wikipedia article, scroll down to "Gauss map definition".

Gauss map is holomorphic (as a map to the Riemann sphere) if the surface is minimal. This is Lemma 8.3 in the book of Osserman, a Survey of Riemann surfaces. In fact, if you replace "embedded" by "immersed" then the converse is also true (see Wikipedia article, https://en.wikipedia.org/wiki/Minimal_surface scroll down to "Gauss map definition".