Some pinching and classification theorems for minimal submanifolds. (English) Zbl 0811.53060

The author proves that the sectional curvature \(K\) and the scalar curvature \(\tau\) of a minimal submanifold of a Euclidean space satisfy the inequality \(K(\pi) \geq {1\over 2} \tau (p)\) for any plane section \(\pi \subset T_ p(M)\), \(p \in M\). Then, he constructs examples of minimal submanifolds of a Euclidean space which satisfy \(\inf K = {1\over 2} \tau\) and classifies minimal submanifolds in Euclidean space which satisfy \(\inf K = {1\over 2} \tau\).
Reviewer: M.Okumura (Urawa)


53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
Full Text: DOI


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