Schwarzian derivatives, projective structures, and the Weil–Petersson gradient flow for renormalized volume
نویسندگان
چکیده
منابع مشابه
Projective Connections and Schwarzian Derivatives for Supermanifolds, and Batalin-vilkovisky Operators
We extend the notion of a Thomas projective connection (a projective equivalence class of linear connections) for supermanifolds. As a by-product, we arrive at a generalisation of the multidimensional Schwarzian derivative for the super case which was previously unknown. This is combined with our previous construction of a Laplacian on the algebra of densities for a projectively connected manif...
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In every textbook on elementary function theory you can find a definition of Schwarzian derivative {z; x} = 1 2 z z − 1 4 z z 2 , where = d/dx, of a non-constant function z = z(x) with respect to x. You would also find an exercise to show (0.1) [PGL(2)-invariance] If a, b, c, and d are constants satisfying ad − bc = 0, then az + b cz + d ; x = {z; x}. (0.2) {z; x} = 0 if and only if z(x) = (ax ...
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ژورنال
عنوان ژورنال: Duke Mathematical Journal
سال: 2019
ISSN: 0012-7094
DOI: 10.1215/00127094-2018-0061