the metric is the sum of the metric on the subspaces: where and are the metrics, respectively, on the subspaces A and B. Connection and curvature The fact that the metric can be derived from the Kähler potential means that the Christoffel symbols and the curvature tensors contain a lot of symmetries, and can be given a particularly simple form: The Christoffel symbols, in the local affine coordinates, are given by The Riemann tensor is also particularly simple: The Ricci tensor is Pronunciation A common pronunciation mistake, made especially by native English speakers, is to assume that Study is pronounced the same as the verb to study. Since it is actually a German name, the correct way to pronounce the u in Study is the same as the u in Fubini. Furthermore, the S in Study is pronounced like the sh in Fisher. In terms of phonetics: ʃtuːdi. See also Non-linear sigma model Kaluza–Klein theory Arakelov height References . Projective geometry Complex manifolds Symplectic geometry Structures on manifolds Quantum mechanics