Isometries of the space of Sasaki potentials

• Autores: Thomas Franzinetti
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 26, Nº 2, 2025, págs. 645-658
• Idioma: inglés
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• Resumen

  • Given any two Kahler manifolds ¨ X1 and X2, L. Lempert recently proved that if their spaces of Kahler potentials are isometric with respect to the ¨ Mabuchi metric, then X1 and X2 must be diffeomorphic. We prove that this is no longer the case for Sasaki manifolds. Then, considering regular Sasaki manifolds M1 and M2, we prove that if the spaces of potentials are isometric, then M1 and M2 must have, among other things, the same universal covering space.

    Finally, getting rid of the regularity assumption on M1 and M2, we investigate the consequences of the existence of affine Mabuchi isometries: this leads to a family of Sasaki isospectral structures.