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  1. Applied Mathematics-A Journal of Chinese Universities
  2. Applied Mathematics-A Journal of Chinese Universities : Volume 23
  3. Applied Mathematics-A Journal of Chinese Universities : Volume 23, Issue 2, June 2008
  4. An optimal rigidity theorem for complete submanifolds in a sphere
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Applied Mathematics-A Journal of Chinese Universities : Volume 32
Applied Mathematics-A Journal of Chinese Universities : Volume 31
Applied Mathematics-A Journal of Chinese Universities : Volume 30
Applied Mathematics-A Journal of Chinese Universities : Volume 29
Applied Mathematics-A Journal of Chinese Universities : Volume 28
Applied Mathematics-A Journal of Chinese Universities : Volume 27
Applied Mathematics-A Journal of Chinese Universities : Volume 26
Applied Mathematics-A Journal of Chinese Universities : Volume 25
Applied Mathematics-A Journal of Chinese Universities : Volume 24
Applied Mathematics-A Journal of Chinese Universities : Volume 23
Applied Mathematics-A Journal of Chinese Universities : Volume 23, Issue 4, December 2008
Applied Mathematics-A Journal of Chinese Universities : Volume 23, Issue 3, September 2008
Applied Mathematics-A Journal of Chinese Universities : Volume 23, Issue 2, June 2008
Interactional models for adults of two populations with maturation delays
Existence of two periodic solutions of a ratio-dependent Holling-Taner model with infinite delay and prey harvest
Multiple positive solutions for a class of nonlinear four-point boundary value problem with p-Laplacian
Asymptotic stability of solutions to the nonisentropic hydrodynamic model for semiconductors
$$ \mathcal{P} $$ -optimal robust designs for multiresponse approximately linear regression
Nonparametric estimation for contamination distribution
A weak invariance principle for self-normalized products of sums of mixing sequences
A general result on precise asymptotics for linear processes of positively associated sequences
A note on self-normalized Dickey-Fuller test for unit root in autoregressive time series with GARCH errors
Pointwise characterization for combinations of Szász-Mirakjan operators
Some notes on a conjecture of Zygmund
An optimal rigidity theorem for complete submanifolds in a sphere
Some remarks on pseudo-umbilical totally real submanifolds in a complex projective space
Stability of Hausdorff dimension of Axiom A attractors under random perturbations
Generalized normal matrices
A note about the cyclotomic polynomial Φ$_{ pq }$(x) and some related results
Applied Mathematics-A Journal of Chinese Universities : Volume 23, Issue 1, March 2008
Applied Mathematics-A Journal of Chinese Universities : Volume 22
Applied Mathematics-A Journal of Chinese Universities : Volume 21
Applied Mathematics-A Journal of Chinese Universities : Volume 20
Applied Mathematics-A Journal of Chinese Universities : Volume 19
Applied Mathematics-A Journal of Chinese Universities : Volume 18
Applied Mathematics-A Journal of Chinese Universities : Volume 17
Applied Mathematics-A Journal of Chinese Universities : Volume 16
Applied Mathematics-A Journal of Chinese Universities : Volume 15
Applied Mathematics-A Journal of Chinese Universities : Volume 14
Applied Mathematics-A Journal of Chinese Universities : Volume 13
Applied Mathematics-A Journal of Chinese Universities : Volume 12

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An optimal rigidity theorem for complete submanifolds in a sphere

Content Provider Springer Nature Link
Author Xu, Hong wei Zhu, Jiao feng
Copyright Year 2008
Abstract It is proved that if M $^{ n }$ is an n-dimensional complete submanifold with parallel mean curvature vector and flat normal bundle in S $^{ n+p }$(1), and if sup$_{ M }$ S < α(n,H), where $$ \alpha (n,{\rm H}) = n + \frac{{n^3 }} {{2(n - 1)}}{\rm H}^2 - \frac{{n(n - 2)}} {{2(n - 1)}}\sqrt {n^2 H^4 + 4(n - 1)H^2 } $$ , then M $_{ n }$ must be the totally umbilical sphere $$ S^n (\frac{1} {{\sqrt {1 + H^2 } }}) $$ . An example to show that the pinching constant α(n,H) appears optimal is given.
Starting Page 219
Ending Page 226
Page Count 8
File Format PDF
ISSN 10051031
Journal Applied Mathematics-A Journal of Chinese Universities
Volume Number 23
Issue Number 2
e-ISSN 19930445
Language English
Publisher SP Editorial Committee of Applied Mathematics - A Journal of Chinese Universities
Publisher Date 2008-06-12
Publisher Place Heidelberg
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword submanifold rigidity flat normal bundle mean curvature Applications of Mathematics Mathematics
Content Type Text
Resource Type Article
Subject Applied Mathematics
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