Who is the father of geometry?

Euclid
Euclid, The Father of Geometry.

Who uses geometry today?

Geometry is used in various daily life applications such as art, architecture, engineering, robotics, astronomy, sculptures, space, nature, sports, machines, cars, and much more. Some of such applications used in daily life are mentioned below: Nature: One of the best examples of geometry in daily life is nature.

Can we live without geometry?

Well Geometry is very important in daily life. Without Geometry things would have been very challenging in Day to day life as well in various technological fields. Lines, Angles, Shapes, 2d & 3d designs plays a vital role in designing of home and commercial infra, mechanical and engineering design.

What is a pseudo Riemannian manifold?

Pseudo-Riemannian manifold. In differential geometry, a pseudo-Riemannian manifold (also called a semi-Riemannian manifold) is a generalization of a Riemannian manifold in which the metric tensor need not be positive-definite, but need only be a non-degenerate bilinear form, which is a weaker condition.

What is an example of a pseudo-Riemannian space?

The simplest example of a pseudo-Riemannian space is the space $ {} ^ {l} \\mathbf R _ {n} $.

What is a pseudo-Riemannian metric?

Such a metric is called a pseudo-Riemannian metric. Applied to a vector field, the resulting scalar field value at any point of the manifold can be positive, negative or zero. The signature of a pseudo-Riemannian metric is (p, q), where both p and q are non-negative.

What is sectional curvature in pseudo-Riemannian space?

In a pseudo-Riemannian space the sectional curvature is defined for every non-degenerate two-dimensional direction. It can be interpreted as the curvature of the geodesic (non-isotropic) $ 2 $- surface drawn through the given point in the given two-dimensional direction.