Murakami–Yano formula

The Murakami–Yano formula is a result in differential geometry, specifically concerning the relationship between the curvature of a Riemannian manifold and the behavior of the volume of the manifold under certain geometric transformations. Named after mathematicians Hideo Murakami and Yoshihiro Yano, the formula provides a way to compute the derivative of the volume of a Riemannian manifold when the metric is varied.