caa a22 4500 605461570 CHVBK 20210128100244.0 cr unu---uuuuu 210128e20150301xx s 000 0 eng 10.1007/s10114-015-3573-5 doi (NATIONALLICENCE)springer-10.1007/s10114-015-3573-5 Fang Jian Department of Mathematics, Tongji University, 200092, Shanghai, P. R. China aut On Laguerre form and Laguerre isoparametric hypersurfaces [Elektronische Daten] [Jian Fang] Let x: M n−1 → ℝ n be an umbilical free hypersurface with non-zero principal curvatures. M is called Laguerre isoparametric if it satisfies two conditions, namely, it has vanishing Laguerre form and has constant Lauerre principal curvatures. In this paper, under the condition of having constant Laguerre principal curvatures, we show that the hypersurface is of vanishing Laguerre form if and only if its Laguerre form is parallel with respect to the Levi-Civita connection of its Laguerre metric. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg, 2015 Laguerre isoparametric hypersurface nationallicence Laguerre second fundamental form nationallicence Laguerre metric nationallicence Laguerre form nationallicence parallel Laguerre form nationallicence Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/3(2015-03-01), 501-510 1439-8516 31:3<501 2015 31 10114 https://doi.org/10.1007/s10114-015-3573-5 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/s10114-015-3573-5 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Fang Jian Department of Mathematics, Tongji University, 200092, Shanghai, P. R. China aut NATIONALLICENCE 773 0- Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/3(2015-03-01), 501-510 1439-8516 31:3<501 2015 31 10114