caa a22 4500 445835664 CHVBK 20180317145329.0 cr unu---uuuuu 170323e20110801xx s 000 0 eng 10.1007/s00209-010-0709-2 doi (NATIONALLICENCE)springer-10.1007/s00209-010-0709-2 The diastatic exponential of a symmetric space [Elektronische Daten] [Andrea Loi, Roberto Mossa] Let (M, g) be a real analytic Kähler manifold. We say that a smooth map Exp p : W → M from a neighbourhood W of the origin of T p M into M is a diastatic exponential at p if it satisfies $$\begin{array}{lll} &\,\,\left(d{\rm Exp}_p\right)_0 & = {\rm id}_{T_pM},\\ D_p&\left({\rm Exp}_p \left(v\right) \right) & = g_p\left(v, v\right),\,\,\forall v\in W, \end{array}$$ where D p is Calabi's diastasis function at p (the usual exponential exp p obviously satisfied these equations when D p is replaced by the square of the geodesics distance from p). In this paper we prove that for every point p of an Hermitian symmetric space of noncompact type M there exists a globally defined diastatic exponential centered in p which is a diffeomorphism and it is uniquely determined by its restriction to polydisks. An analogous result holds true in an open dense neighbourhood of every point of M *, the compact dual of M. We also provide a geometric interpretation of the symplectic duality map (recently introduced in Di Scala and Loi (Adv Math 217:2336-2352, 2008)) in terms of diastatic exponentials. As a byproduct of our analysis we show that the symplectic duality map pulls back the reproducing kernel of M * to the reproducing kernel of M. Springer-Verlag, 2010 Kähler metrics nationallicence Bounded symmetric domains nationallicence Symplectic duality nationallicence Jordan triple systems nationallicence Bergman operator nationallicence Loi Andrea Dipartimento di Matematica e Informatica, Università di Cagliari, Via Ospedale 72, 09124, Cagliari, Italy aut Mossa Roberto Dipartimento di Matematica e Informatica, Università di Cagliari, Via Ospedale 72, 09124, Cagliari, Italy aut Mathematische Zeitschrift Springer-Verlag 268/3-4(2011-08-01), 1057-1068 0025-5874 268:3-4<1057 2011 268 209 https://doi.org/10.1007/s00209-010-0709-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-010-0709-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Loi Andrea Dipartimento di Matematica e Informatica, Università di Cagliari, Via Ospedale 72, 09124, Cagliari, Italy aut NATIONALLICENCE 700 1- Mossa Roberto Dipartimento di Matematica e Informatica, Università di Cagliari, Via Ospedale 72, 09124, Cagliari, Italy aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 268/3-4(2011-08-01), 1057-1068 0025-5874 268:3-4<1057 2011 268 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer