2022/05/03 by Bo Berndtsson, Berndtsson, Bo · 2 citations
Mathematics · Physics and Astronomy · #Geometry and complex manifolds #Geometric Analysis and Curvature Flows #Advanced Differential Geometry Research
paper · pdf · doi:10.48550/arxiv.2205.01339
We give some remarks on geodesics in the space of Kähler metrics that are defined for all time. Such curves are conjecturally induced by holomorphic vector fields, and we show that this is indeed so for regular geodesics, whereas the question for generalized geodesics is still open (as far as we know). We also give a result about the derivative of such geodesics which implies a variant of a theorem of Atiyah and Guillemin-Sternberg on convexity of the image of certain moment maps.