caa a22 4500 606201041 CHVBK 20210128100946.0 cr unu---uuuuu 210128e20150901xx s 000 0 eng 10.1007/s00025-014-0419-x doi (NATIONALLICENCE)springer-10.1007/s00025-014-0419-x The Generalized Cayley Hypersurfaces and Their Geometrical Characterization [Elektronische Daten] [Cece Li, Dong Zhang] In this paper, we study a whole family of n-dimensional equiaffine homogeneous hypersurfaces with a parameter α, constructed by Eastwood and Ezhov (Proc Steklov Inst Math 253:221-224, 2006), called the generalized Cayley hypersurfaces. By introducing a new parametrization we find that the generalized Cayley hypersurfaces are improper affine hypersphere with flat affine metric and vanishing Pick invariant, whose difference tensor K satisfies $${\nabla^{(\alpha)}K=0 \,\,{\rm and}\,\, K^{n-1} \neq 0}$$ ∇ ( α ) K = 0 and K n - 1 ≠ 0 , where the affine $${\alpha{\rm -connection}\,\, \nabla^{(\alpha)}}$$ α - connection ∇ ( α ) of information geometry is first introduced on affine hypersurface for each $${\alpha\in\mathbb{R}}$$ α ∈ R . As main result, we establish a characterization of the generalized Cayley hypersurfaces by the last two properties for some nonzero constant α. Springer Basel, 2014 The generalized Cayley hypersurfaces nationallicence geometrical characterization nationallicence parallel difference tensor nationallicence affine α -connection nationallicence Li Cece School of Mathematics and Statistics, Henan University of Science and Technology, 471023, Luoyang, People's Republic of China aut Zhang Dong School of Mathematical Sciences, Peking University, 100871, Beijing, People's Republic of China aut Results in Mathematics Springer Basel 68/1-2(2015-09-01), 25-44 1422-6383 68:1-2<25 2015 68 25 https://doi.org/10.1007/s00025-014-0419-x 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/s00025-014-0419-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Li Cece School of Mathematics and Statistics, Henan University of Science and Technology, 471023, Luoyang, People's Republic of China aut NATIONALLICENCE 700 1- Zhang Dong School of Mathematical Sciences, Peking University, 100871, Beijing, People's Republic of China aut NATIONALLICENCE 773 0- Results in Mathematics Springer Basel 68/1-2(2015-09-01), 25-44 1422-6383 68:1-2<25 2015 68 25