Search Results for ""

A surface on which the Gaussian curvature K is everywhere positive. When K is everywhere negative, a surface is called anticlastic. A point at which the Gaussian curvature is ...

Two curves both containing the point P are tangent at P if they share the same tangent line at P.

Let the speed sigma of a closed curve on the unit sphere S^2 never vanish. Then the tangent indicatrix, also called the tantrix, tau=(sigma^.)/(|sigma^.|) is another closed ...

Also known as the total curvature. The linear element of the indicatrix ds_P=sqrt(ds_T^2+ds_B^2).

An umbilic point, also called simply an umbilic, is a point on a surface at which the curvature is the same in any direction.

v=(dr)/(dt), (1) where r is the radius vector and d/dt is the derivative with respect to time. Expressed in terms of the arc length, v=(ds)/(dt)T^^, (2) where T^^ is the unit ...

An natural equation which expresses a curve in terms of its arc length s and tangential angle phi.

The anti-self-dual Yang-Mills equation is the system of partial differential equations ...

Using the notation of Byerly (1959, pp. 252-253), Laplace's equation can be reduced to (1) where alpha = cint_c^lambda(dlambda)/(sqrt((lambda^2-b^2)(lambda^2-c^2))) (2) = ...

A Lyapunov function is a scalar function V(y) defined on a region D that is continuous, positive definite, V(y)>0 for all y!=0), and has continuous first-order partial ...