surfaces

1. I Variation of geometrical quantities under infinitesimal deformation

This question is about 2-d surfaces embedded inR3 It's easy to find information on how the metric tensor changes when $$x_{\mu}\rightarrow x_{\mu}+\varepsilon\xi(x)$$ So, what about the variation of the second fundamental form, the Gauss and the mean curvature? how they change? I found...
2. How do I parameterize these surfaces?

1. Homework Statement Parameterize $S={ S }_{ 1 }\bigcup { { S }_{ 2 } }$, where $S_1$ is the surface with equation $x^2+y^2=4$ bounded above by the graph of $2y+z=6$ and below by the $xy$ plane. $S_2$ is the bottom disk 2. Homework Equations 3. The Attempt at a Solution ##{ S...
3. Help please -- Problem of hydrostatics force in flat surfaces

1. Homework Statement 2. Homework Equations 3. The Attempt at a Solution I could know the pressure in point B If I calculate the heigh of pressure I got: But I don't know where is my free surface in the container 3, is it down?? I don't know how to keep doing it.....