RTMP Seminar: Riemann geometry without indices

Seminar | October 23 | 4-5 p.m. | 939 Evans Hall

 Vladimir Fock, Université de Strasbourg

 Department of Mathematics

The talk will be devoted to a well know subject — basic theorems of Riemann geometry — Bianchi identities, conformal invariance of the Weyl tensor, variation of the Hilbert functional and some others. We suggest a formalism to give a few line proofs of these statements based on formulation of Riemann geometry as a gauge theory in terms of Clifford forms as well as the action of a group $\mathfrak{sl}(2) \times \mathfrak{sl}(2)$ thereon. Analogous formalism for Kähler geometry involves the action of the affine group $\widehat{\mathfrak{sl}}(4)$. Joint work with P.Goussard.

 shapiro@math.berkeley.edu