Abstract
A Riemannian metric g on a flat manifold M with flat connection D is called a Hessian metric if it is locally expressed by the Hessian of local functions ϕ with respect to the affine coordinate systems, that is, g = Ddϕ Such pair (D, g), g, and M are called a Hessian structure, a Hessian metric, and a Hessian manifold, respectively [S7].
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Shima, H. (2013). Geometry of Hessian Structures. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2013. Lecture Notes in Computer Science, vol 8085. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40020-9_4
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DOI: https://doi.org/10.1007/978-3-642-40020-9_4
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