Liouville's equation

（重定向自Liouville equation）

For Liouville's equation in dynamical systems, see Liouville's theorem (Hamiltonian).

For Liouville's equation in quantum mechanics, see Von Neumann equation.

In differential geometry, Liouville's equation, named after Joseph Liouville, is the nonlinear partial differential equation satisfied by the conformal factor $f$ of a metric $f^2(\mathrm{d}x^2 + \mathrm{d}y^2)$ on a surface of constant Gaussian curvature $K$ :

where $\Delta_0$ is the flat Laplace operator.

单词	Liouville equation
释义	Liouville equation 英语百科 Liouville's equation （重定向自Liouville equation） For Liouville's equation in dynamical systems, see Liouville's theorem (Hamiltonian). For Liouville's equation in quantum mechanics, see Von Neumann equation. In differential geometry, Liouville's equation, named after Joseph Liouville, is the nonlinear partial differential equation satisfied by the conformal factor $f$ of a metric $f^2(\mathrm{d}x^2 + \mathrm{d}y^2)$ on a surface of constant Gaussian curvature $K$ : where $\Delta_0$ is the flat Laplace operator.
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