Bun’kova, E. Yu The differential-geometric structure of the universal bundle of elliptic curves. (English. Russian original) Zbl 1254.14035 Russ. Math. Surv. 66, No. 4, 816-818 (2011); translation from Usp. Mat. Nauk 66, No. 4, 185-186 (2011). Let \(\mathcal{E}_1 \rightarrow {\mathbb C}^2\) be the bundle of elliptic curves whose fiber over \((g_2,g_3) \in {\mathbb C}^2\) is the curve with affine part \(\left\{ (x,y) \in {\mathbb C}^2 : y^2 = 4 x^3 - g_2 x - g_3 \right\}\). The paper explicitly computes, as power series expansions with recursion formulae, the symmetric cometrics on \({\mathbb C}^2\) for which the Gauss-Manin connection on \({\mathcal E}_1\) is a metric connection A generalization of some of the results to the bundle of genus two curves is also given. Reviewer: Imin Chen (Burnaby) Cited in 1 Document MSC: 14H52 Elliptic curves 14H60 Vector bundles on curves and their moduli 53B15 Other connections Keywords:elliptic curves; Gauss-Manin connection; symmetric cometrics PDFBibTeX XMLCite \textit{E. Y. Bun'kova}, Russ. Math. Surv. 66, No. 4, 816--818 (2011; Zbl 1254.14035); translation from Usp. Mat. Nauk 66, No. 4, 185--186 (2011) Full Text: DOI