English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

. Let x : M n−1 → R n (n ≥ 4) be an umbilical free hyper-surface with non-zero principal curvatures. Then x is associated witha Laguerre metric g, a Laguerre tensor L, a Laguerre form C, and aLaguerre second fundamental form B, which are invariants of x underLaguerre transformation group. We denote the Laguerre scalar curvatureby R and the trace-free Laguerre tensor by L˜ := L− 1n−1 tr(L)g. Inthis paper, we prove a local classication result under the assumption ofparallel Laguerre form and an inequality of the typekL˜k ≤ cR,where c= 1(n−3) √ (n−2)(n−1) is appropriate real constant, depending onthe dimension. 1. IntroductionLet x : M n−1 → R n be an umbilical free hypersurface with non-zero princi-pal curvatures. Let ξ : M → S n−1 be its unit normal. Let {e 1 ,e 2 ,...,e n−1 }be the orthonormal basis for TM with respect to dx · dx, consisting of unitprincipal vectors. Let r i = 1k i , r = r 1 +r 2 +···+r n−1 n−1 be the curvature radius andmean curvature radius of x respectively, where k

LAGUERRE CHARACTERIZATION OF SOME HYPERSURFACES