Gaussian curvature at the hyperelliptic Weierstrass points

2007/03/03 by Abel Castorena, Castorena, Abel
Mathematics · #53A55 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53A55

paper · pdf · doi:10.48550/arxiv.math/0703075

The paper has been withdrawn by the author

arxiv created 2012/03/05 · arxiv updated 2012/03/06

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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