Long geodesics in the space of K\"ahler metrics
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Publication:6398113
DOI10.1007/S10476-022-0140-ZarXiv2205.01339MaRDI QIDQ6398113
Publication date: 3 May 2022
Abstract: We give some remarks on geodesics in the space of K"ahler 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.
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