Geometry VI: Riemannian Geometry

By M. Postnikov. 2001

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Exponential Barycenters of the Canonical Cartan Connection and Invariant Means on Lie Groups (2013, unknown): “Most results of this section can be found in the more modern (and quite comprehensive) presentation of differential geometry and Lie groups of Postnikov [58].”
A Riemannian geometry with complete geodesics for the set of positive semidefinite matrices of fixed rank (2013, background): “The extremals of S will be exactly the geodesics A(t) (Postnikov, 2001, Prop.”
Weakly Z-symmetric manifolds (2011, background): “ose divergence has the form (26), with trivial Codazzi tensor: (29) ∇mKjkl m = A∇ mRjkl m +B(gkl∇j −gjl∇k)R. They are the projective curvature tensor Pjklm [18], the conformal curvature tensor Cjkl m [27], the concircular tensor C˜ jkl m [28, 32], the conharmonic tensor Njklm [26, 30] and the quasi ”