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Abstract: In Proposition 4.1 a characterization is given of Hessian Riemannian structures in terms of a natural connection in the general linear group , which is viewed as a principal SO(n)-bundle over the space of positive definite symmetric n \Theta n-matrices. For n = 2, Proposition 5.3 contains an interpretation of the curvature of a Hessian Riemannian structure at a given point, in terms of an umbilic point of a related surface in R . (Update)
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BibTeX entry: (Update)
@misc{ duistermaat-hessian,
author = "J.J. Duistermaat",
title = "On Hessian Riemannian Structures",
url = "citeseer.ist.psu.edu/duistermaat99hessian.html" }
Citations (may not include all citations):9 Nomizu: Foundations of Differential Geometry (context) - Kobayashi - 1963
8 Tu: Differential Forms in Algebraic Topology (context) - Bott - 1982
6 Nemirovskii: Interior-Point Polynomial Algorithms in Convex .. (context) - Nesterov - 1994
5 Mathematische Zeitschrift (context) - Hamburger, mit et al. - 1924
5 Scuola Norm (context) - Hitchin, space et al. - 1997
5 Moscow Math (context) - Vinberg, of et al. - 1963
4 Springer Verlag (context) - Blaschke, Differentialgeometrie - 1929
2 Differential Geometry and its Applications (context) - Shima, Yagi et al. - 1997
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