Differential geometry is the field of mathematics that uses the techniques of calculus and linear algebra to study problems in geometry, particularly those involving curves and surfaces. It plays a crucial role in understanding the geometry of differentiable manifolds and has applications in physics, particularly in the theory of general relativity and modern theoretical physics.

Differential Geometry

Differential geometry

techniques of calculus

Linear algebra is a branch of mathematics that deals with vector spaces and linear mappings between these spaces, focusing on the study of lines, planes, and subspaces. It is fundamental in various scientific fields, providing tools for solving systems of linear equations, performing transformations, and analyzing vector spaces and matrices.

linear algebra

problems in geometry

curves and surfaces

geometry of differentiable manifolds

applications in physics

theory of general relativity

modern theoretical physics

Exterior Derivative

Definition and Examples of Covariant and Contravariant Vectors

Geometric Analysis of the Laplace-Beltrami Operator

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