caa a22 4500 606201017 CHVBK 20210128100946.0 cr unu---uuuuu 210128e20150901xx s 000 0 eng 10.1007/s00025-014-0426-y doi (NATIONALLICENCE)springer-10.1007/s00025-014-0426-y On the Equiaffine Symmetric Hyperspheres [Elektronische Daten] [Xingxiao Li, Guosong Zhao] We introduce and study the equiaffine symmetric hyperspheres. For the first step we consider the locally strongly convex ones. In fact, by the idea used by H. Naitoh, we provide in this paper a direct proof of the complete classification for those affine symmetric hyperspheres. Then, via an earlier result of the first author, we are able to provide an alternative proof for the classification theorem of the affine hypersurface with parallel Fubini-Pick forms, which has already been established by Z. J. Hu etal. in a totally different way. Springer Basel, 2014 Equiaffine hypersphere nationallicence affine metric nationallicence Fubini-Pick form nationallicence symmetric space nationallicence affine symmetric hypersurface nationallicence Li Xingxiao School of Mathematics and Information Sciences, Henan Normal University, 453007, Xinxiang, Henan, People's Republic of China aut Zhao Guosong School of Mathematics, Sichuan University, 610064, Chengdu, Sichuan, People's Republic of China aut Results in Mathematics Springer Basel 68/1-2(2015-09-01), 117-142 1422-6383 68:1-2<117 2015 68 25 https://doi.org/10.1007/s00025-014-0426-y text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00025-014-0426-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Li Xingxiao School of Mathematics and Information Sciences, Henan Normal University, 453007, Xinxiang, Henan, People's Republic of China aut NATIONALLICENCE 700 1- Zhao Guosong School of Mathematics, Sichuan University, 610064, Chengdu, Sichuan, People's Republic of China aut NATIONALLICENCE 773 0- Results in Mathematics Springer Basel 68/1-2(2015-09-01), 117-142 1422-6383 68:1-2<117 2015 68 25