The Latin word curvature came to our tongue What curvature. The concept refers to the curved condition (bent or crooked). The idea of curvature is also used with respect to the deviation that has a curved line with respect to a straight line.
For example: “The criminals tried to take advantage of the curvature of the wall to hide, but they were discovered”, “A bad body posture can cause, in the long term, the curvature of the column vertebral “, “The curvature of the screen surprised the public”.
If someone talks about the curvature of a television, to cite one case, they are referring to the fact that its screen is not straight. The curvature of a telephone cellular (mobile), meanwhile, is linked to its curved edges. In these cases, the curvature can represent both an aesthetic and a functional aspect, or a fusion of both. Regardless of the purpose of this feature in an appliance, electronic device or automobile, among other products, fashion trends make it inevitable that its duration is limited, so sooner or later the curvature is replaced by the angular edges, and vice versa.
In the field of geometry and mathematics, curvature can be the magnitude or the number which measures this quality. It is, in this framework, the amount that a geometric object deviates from a line or plane.
The notion of space-time curvature derives from general relativity theory, which postulates that the gravity it is an effect of the curved geometry that spacetime has. According to this theory, bodies that are in a gravitational field make a curved path in space. The curvature of space-time is measured according to the so-called curvature tensor or Riemann tensor.
The curvature displacement, on the other hand, is a theory which indicates that a vehicle could travel at a speed greater than the speed of light from a distortion that generates a greater curvature in space-time.
There is a quantity called Radius of curvature which is used to measure the curvature of an object belonging to geometry as if it were a surface, a curved line or, more generally, a differentiable variety which is in a euclidean space.
If we take an object or a curved line as a reference, its radio curvature is a geometric quantity that we can define at each of its points, and it is equivalent to the inverse of the absolute value of curvature at all of them. We must not forget that curvature is the alteration that the direction of the vector tangent to a given curve goes through as we move along it.
One of the measurements that we can do on a given surface is the gaussian curvature, a number belonging to the set of reals that represents the intrinsic curvature for each of the regular points. It is possible to calculate it starting from the determinants of the two fundamental forms of the surface.
The first fundamental form of the surface is a 2-covariant tensor presenting symmetry and it is defined in the tangent space to each of its points; it is the metric tensor (that is, of rank 2, used to define concepts such as volume, angle and distance) that the Euclidean metric induces on the surface. The second, on the other hand, is the projection of the covariant derivative that is carried out on the normal vector to the surface, and is induced by the first fundamental form.
Gaussian curvature is generally different at each point on the surface and is related to its principal curvatures. The sphere It is a special case of a surface, since in all its points it presents the same curvature.