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A non-existence theorem for isometric immersions

Ranjbar Motlagh, A ; Sharif University of Technology | 2009

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  1. Type of Document: Article
  2. DOI: 10.1016/j.geomphys.2008.11.001
  3. Publisher: 2009
  4. Abstract:
  5. Let f : M {long rightwards arrow} over(M, -) be an isometric immersion between Riemannian manifolds. For certain conditions on M and over(M, -) in terms of curvatures and external diameter, we extend the non-embedding theorem of Chern and Kuiper to the isometric immersions of non-compact manifolds. Also, our results generalize and improve the main results of Jorge and Koutroufiotis [L. Jorge, D. Koutroufiotis, An estimate for the curvature of bounded submanifolds, Amer. J. Math. 103 (4) (1981) 711-725] and Veeravalli [A. R. Veeravalli, A sharp lower bound for the Ricci curvature of bounded hypersurfaces in space forms, Bull. Austral. Math. Soc. 62 (1) (2000) 165-170]. © 2008 Elsevier B.V. All rights reserved
  6. Keywords:
  7. Curvature ; Embedding ; Isometric immersion ; Maximum principle
  8. Source: Journal of Geometry and Physics ; Volume 59, Issue 3 , 2009 , Pages 263-266 ; 03930440 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/pii/S0393044008001812