We consider a curve in the xz plane and rotate it around the z-axis to form a surface of revolution. We assume that the curve is already in arclength parameter, then we parameterize the surface. With this parameterization we compute the first and second fundamental forms of the surface.
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First and Second Fundamental Forms of Surfaces of Revolution Source
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mike the mathematicianmike dabkowski mathfirst fundamental formsecond fundamental formsurface of revolutionfirst fundamental form of a surface or revolutionsecond fundamental form of a surface of revolutionparameterize a surface of revolutionsurface of revolution first fundamental formsecond fundamental form in differential geometryFirst and Second Fundamental Form Intuition1st and 2nd fundamental form of surface of revolutionnormal to surface of revolution
