Compact hypersurfaces in a unit sphere with infinite fundamental group
نویسندگان
چکیده
منابع مشابه
Compact 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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Let M be an n(n ≥ 3)-dimensional complete connected hypersurface in a unit sphere S(1). In this paper, we show that (1) if M has non-zero mean curvature and constant scalar curvature n(n−1)r and two distinct principal curvatures, one of which is simple, then M is isometric to the Riemannian product S( √ 1− c2) × Sn−1(c), c = n−2 nr if r ≥ n−2 n−1 and S ≤ (n−1)n(r−1)+2 n−2 + n−2 n(r−1)+2 . (2) i...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 2003
ISSN: 0030-8730
DOI: 10.2140/pjm.2003.212.49