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Gaussian curvature at the hyperelliptic Weierstrass points

Abel Castorena
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Abstract

Let C be a hyperelliptic Riemann surface. We show that the hyperelliptic Weierstrass points of C are non-degenerated critical points of Morse index +2 of the curvature function K of the Theta metric on C (called also Bergman metric). When the genus of C is two, we compute all critical points of K and we show in this case that K is a Morse function.

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Abel Castorena. 2007-03-03. Gaussian curvature at the hyperelliptic Weierstrass points. https://arxiv.org/abs/math/0703075

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