Rigidity of spheres in Riemannian manifolds and a non-embedding theorem. (English) Zbl 1032.53047
The author studies isometric immersions between Riemannian manifolds. He obtains sufficient conditions in terms of curvatures and the external diameter in order that the image of the immersion is contained in a geodesic sphere. He uses this result to obtain non-embedding theorems.
Reviewer: Gerhard Knieper (Bochum)
MSC:
| 53C40 | Global submanifolds |
| 53C24 | Rigidity results |
| 53C42 | Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) |
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