Curves and Surfaces

Consider a surface of revolution with respect to $z$-axis and suppose that the generating curve $s\mapsto (f(t),0,g(t))$ is parametrized by...

Consider the right cylinder $X(u,v)=\alpha(u)+v\vec{a}$, where $\alpha$ is a regular curve contained in a orthogonal plane to the vector $\...

A geodesic in a plane $P$ writes as $\gamma(s)=p+s v$, $p\in P$ and $v\in T_pP=P$. Then the exponential map is simply $$exp(v)=p+v$$ that...

Following the above entry, the case $H=0$ is known: the plane and the catenoid are the only rotational minimal surfaces . If $H=0$, then we...

We calculate the equation of a surface of revolution with constant mean curvature $H$. Without loss of generality, we suppose that the prof...

We know that if $K(p)>0$ at one pint, then the surface locally in one side of its affine tangent plane. On the other hand, if the surfac...

The explicit computation of the asymptotic curves and lines of a curvature in a given surface uses parametrizations. Thus their computati...