# Metric tensor

In the mathematical field of differential geometry, a metric tensor allows defining distances and angles near each point of a surface, in the same way as inner product allows defining distances and angles in Euclidean spaces. More precisely, a metric tensor at a point of a manifold is a bilinear form defined on the tangent space at this point.
Volume form
In mathematics, a volume form or top-dimensional form is a differential form of degree equal to the differentiable manifold dimension. Thus on a manifold of dimension , a volume form is an -form. It is an element of the space of sections of the line
Tensor (intrinsic definition)
In mathematics, the modern component-free approach to the theory of a tensor views a tensor as an abstract object, expressing some definite type of multilinear concept. Their properties can be derived from their definitions, as linear maps or more
Levi-Civita parallelogramoid
In the mathematical field of differential geometry, the Levi-Civita parallelogramoid is a quadrilateral in a curved space whose construction generalizes that of a parallelogram in the Euclidean plane. It is named for its discoverer, Tullio Levi-Civita
Monge cone
In the mathematical theory of partial differential equations (PDE), the Monge cone is a geometrical object associated with a first-order equation. It is named for Gaspard Monge. In two dimensions
Fubini–Study metric
In mathematics, the Fubini–Study metric is a Kähler metric on projective Hilbert space, that is, on a complex projective space CPn endowed with a Hermitian form. This metric was originally described in 1904 and 1905 by Guido Fubini and Eduard Study
Riesz transform
In the mathematical theory of harmonic analysis, the Riesz transforms are a family of generalizations of the Hilbert transform to Euclidean spaces of dimension d > 1. They are a type of singular integral operator, meaning that they are given by a
Conformal geometry
In mathematics, conformal geometry is the study of the set of angle-preserving (conformal) transformations on a space
Complex projective space
In mathematics, complex projective space is the projective space with respect to the field of complex numbers. By analogy, whereas the points of a real projective space label the lines through the origin of a real Euclidean space, the points of a complex
Monge equation
In the mathematical theory of partial differential equations, a Monge equation, named after Gaspard Monge, is a first-order partial differential equation for an unknown function u in the independent variables x1
Della Dumbaugh
Della Jeanne Dumbaugh is an American mathematician and historian of mathematics, focusing on the history of algebra and number theory. She is a professor of mathematics at the University of Richmond, and the editor-in-chief of The American Mathematical