A **quadratic differential** is a mathematical concept that arises primarily in the fields of complex analysis and differential geometry, often used to study the properties of Riemann surfaces and their associated geometric structures. In a more formal description, a quadratic differential on a Riemann surface can be seen as a section of the tensor product of the cotangent bundle with itself, specifically a differential form of type (2,0).
Articles by others on the same topic
A section of the square of the canonical bundle, locally ; its coefficient changes by the square of the coordinate derivative. A holomorphic quadratic differential has holomorphic coefficient, and its flat metric of a quadratic differential is .