Compact minimal submanifolds of a sphere with positive Ricci curvature
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This article is published in Journal of The Mathematical Society of Japan.The article was published on 1979-04-01 and is currently open access. It has received 40 citations till now. The article focuses on the topics: Scalar curvature & Riemann curvature tensor.read more
Citations
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Journal ArticleDOI
Geometric, topological and differentiable rigidity of submanifolds in space forms
Hongwei Xu,Juan-Ru Gu +1 more
TL;DR: In this article, a differentiable sphere theorem for submanifolds with positive Ricci curvature was obtained, where the curvature of the Ricci surface is defined as the reciprocal of the mean curvature.
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Classification and rigidity of self-shrinkers in the mean curvature flow
Haizhong Li,Yong Wei +1 more
TL;DR: In this article, it was shown that K. Smoczyk's classification theorem for complete self-shrinkers in higher codimension also holds under a weaker condition, and as an application, they gave some rigidity results for self shrinkers in arbitrary-codimension.
Journal ArticleDOI
Curvature pinching for three-dimensional minimal submanifolds in a sphere
TL;DR: In this article, some pinching theorems for the Ricci curvature and scalar curvature of three-dimensional compact minimal submanifolds in a sphere are given.
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Topological and differentiable rigidity of submanifolds in space forms
Hongwei Xu,Juan-Ru Gu +1 more
TL;DR: In this paper, it was shown that if M n (n ≥ 4) is a compact submanifold in F n+p (c), and if RicM > (n − 2)(c + H 2 ), where H is the mean curvature of M, then M is homeomorphic to a sphere.
References
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Book ChapterDOI
Minimal Submanifolds of a Sphere with Second Fundamental Form of Constant Length
TL;DR: In this article, an n-dimensional manifold which is minimally immersed in a unit sphere of dimension n+p is considered. But the manifold is not a sphere, it is a manifold.
Journal ArticleDOI
Minimal Immersions of Spheres into Spheres
TL;DR: In this article, a qualitative description of an important class of closed n-dimensional submanifolds of the m-dimensional sphere, namely, those which locally minimize the n-area in the same way that geodesics minimize the arc length and are themselves locally n-spheres of constant radius r; those r that may appear are called admissible.