منابع مشابه
Linear Weingarten hypersurfaces in a unit sphere
In this paper, by modifying Cheng-Yau$'$s technique to complete hypersurfaces in $S^{n+1}(1)$, we prove a rigidity theorem under the hypothesis of the mean curvature and the normalized scalar curvature being linearly related which improve the result of [H. Li, Hypersurfaces with constant scalar curvature in space forms, {em Math. Ann.} {305} (1996), 665--672].
متن کاملlinear weingarten hypersurfaces in a unit sphere
in this paper, by modifying cheng-yau$'$s technique to complete hypersurfaces in $s^{n+1}(1)$, we prove a rigidity theorem under the hypothesis of the mean curvature and the normalized scalar curvature being linearly related which improve the result of [h. li, hypersurfaces with constant scalar curvature in space forms, {em math. ann.} {305} (1996), 665--672].
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Let M be a compact Minimal hypersurface of the unit sphere S. In this paper we use a constant vector field on R to characterize the Clifford hypersurfaces S (√ l n ) × S mn ) , l + m = n, in S. We also study compact minimal Einstein hypersurfaces of dimension greater than two in the unit sphere and obtain a lower bound for first nonzero eigenvalue λ1 of its Laplacian operator.
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متن کاملCompact Hypersurfaces in a Unit Sphere with Infinite Fundamental Group
It is our purpose to study curvature structures of compact hypersurfaces in the unit sphere S(1). We proved that the Riemannian product S( √ 1 − c2) ×Sn−1(c) is the only compact hypersurfaces in S(1) with infinite fundamental group, which satisfy r ≥ n−2 n−1 and S ≤ (n − 1)n(r−1)+2 n−2 + n−2 n(r−1)+2 , where n(n − 1)r is the scalar curvature of hypersurfaces and c = n−2 nr . In particular, we o...
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ژورنال
عنوان ژورنال: Tsukuba Journal of Mathematics
سال: 1998
ISSN: 0387-4982
DOI: 10.21099/tkbjm/1496163475