Clifford Hypersurfaces in a Unit Sphere
نویسنده
چکیده
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.
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 کاملThe Pinching Constant of Minimal Hypersurfaces in the Unit Spheres
In this paper, we prove that if Mn (n ≤ 8) is a closed minimal hypersurface in a unit sphere Sn+1(1), then there exists a positive constant α(n) depending only on n such that if n ≤ S ≤ n+ α(n), then M is isometric to a Clifford torus, where S is the squared norm of the second fundamental form of M .
متن کاملGeneralized Doubling Constructions for Constant Mean Curvature Hypersurfaces in S
The sphere S contains a simple family of constant mean curvature (CMC) hypersurfaces of the form Λp,q a ≡ S p(a)×Sq( √ 1− a) for p+ q+1 = n and a ∈ (0, 1) called the generalized Clifford hypersurfaces. This paper demonstrates that new, topologically non-trivial CMC hypersurfaces resembling a pair of neighbouring generalized Clifford tori connected to each other by small catenoidal bridges at a ...
متن کاملGeneralized doubling constructions for constant mean curvature hypersurfaces in Sn+1
The sphere Sn+1 contains a simple family of constant mean curvature (CMC) hypersurfaces of the form Ct := Sp(cos t) × Sq(sin t) for p + q = n and t ∈ (0, π2 ) called the generalized Clifford hypersurfaces. This paper demonstrates that new, topologically non-trivial CMC hypersurfaces resembling a pair of neighbouring generalized Clifford tori connected to each other by small catenoidal bridges a...
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...
متن کامل