Analytic saddle spheres in S3 are equatorial Gálvez López, José Antonio Mira, Pablo Tassi, Marcos P. 53A10 53C42 A theorem by Almgren establishes that any minimal 2-sphere immersed in is a totally geodesic equator. In this paper we give a purely geometric extension of Almgren’s result, by showing that any immersed, real analytic 2-sphere in that is saddle, i.e., of non-positive extrinsic curvature, must be an equator of . We remark that, contrary to Almgren’s theorem, no geometric PDE is imposed on the surface. The result is not true for spheres. 2023-11-03T10:37:18Z 2023-11-03T10:37:18Z 2023-10-30 info:eu-repo/semantics/article Gálvez, J.A., Mira, P. & Tassi, M.P. Analytic saddle spheres in are equatorial. Math. Ann. (2023). [https://doi.org/10.1007/s00208-023-02741-4] https://hdl.handle.net/10481/85442 10.1007/s00208-023-02741-4 eng http://creativecommons.org/licenses/by/4.0/ info:eu-repo/semantics/openAccess Atribución 4.0 Internacional Springer Nature