What is Fundamental theorem of Riemannian geometry?

In mathematics, the fundamental theorem of Galois theory is a result that describes the structure of certain types of field extensions in relation to groups. It was proved by Évariste...

In algebraic geometry, universal algebraic geometry generalizes the geometry of rings to geometries of arbitrary varieties of algebras, so that every variety of algebras has its own algebraic geometry. The...

Projective space plays a central role in algebraic geometry. The aim of this article is to define the notion in terms of abstract algebraic geometry and to describe some basic...

In mathematics, a Klein geometry is a type of geometry motivated by Felix Klein in his influential Erlangen program. More specifically, it is a homogeneous space X together with a...

Affine differential geometry is a type of differential geometry in which the differential invariants are invariant under volume-preserving affine transformations. The name affine differential geometry follows from Klein's Erlangen program....

In abstract algebra, the fundamental theorem on homomorphisms, also known as the fundamental homomorphism theorem, or the first isomorphism theorem, relates the structure of two objects between which a homomorphism...

In mathematics, specifically in functional analysis and Hilbert space theory, the fundamental theorem of Hilbert spaces gives a necessarily and sufficient condition for a Hausdorff pre-Hilbert space to be a...

A Riemannian submanifold N of a Riemannian manifold M is a submanifold of M equipped with the Riemannian metric inherited from M. The image of an isometric immersion is a...

Computational anatomy is the study of shape and form in medical imaging. The study of deformable shapes in computational anatomy rely on high-dimensional diffeomorphism groups...