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An example of non-embeddability of the Ricci flow

Safdari, M ; Sharif University of Technology | 2019

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  1. Type of Document: Article
  2. DOI: 10.1007/s10455-018-09646-5
  3. Publisher: Springer Netherlands , 2019
  4. Abstract:
  5. For an evolution of metrics (M, g t ) there is a t-smooth family of embeddings e t : M→ R N inducing g t , but in general there is no family of embeddings extending a given initial embedding e. We give an example of this phenomenon when g t is the evolution of g under the Ricci flow. We show that there are embeddings e inducing g which do not admit of t-smooth extensions to e t inducing g t for any t> 0. We also find hypersurfaces of dim > 2 that will not remain a hypersurface under Ricci flow for any positive time. © 2019, Springer Nature B.V
  6. Keywords:
  7. Hypersurfaces ; Isometric embedding ; Ricci flow
  8. Source: Annals of Global Analysis and Geometry ; Volume 55, Issue 4 , 2019 , Pages 681-685 ; 0232704X (ISSN)
  9. URL: https://link.springer.com/article/10.1007/s10455-018-09646-5