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A Bonnet Theorem for Submanifolds into Rotational Hypersurfaces

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Abstract

In this paper, we prove a version of the fundamental theorem of submanifolds to target manifolds with warped structure.

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References

  1. Bonnet, O.: Mémorie sur la théorie des surfaces applicables sur une surface donnée. J. École Polytech. 42 (1867)

  2. Chen Q., Xiang C.R.: Isometric immersions into warped product spaces. Acta Math. Sin. Engl. Ser. 26(12), 2269–2282 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  3. Dajczer, M.: Submanifolds and isometric immersions. Based on the notes prepared by Mauricio Antonucci, Gilvan Oliveira, Paulo Lima-Filho and Rui Tojeiro. In: Mathematics Lecture Series, vol. 13, pp. x+173. Publish or Perish, Inc., Houston (1990). ISBN: 0-914098-22-5

  4. Daniel B.: Isometric immersions into \({\mathbb{S}^n \times \mathbb{R}}\) and \({\mathbb{H}^n \times \mathbb{R}}\) and applications to minimal surfaces. Trans. Am. Math. Soc. 361, 6255–6282 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  5. Daniel B.: Isometric immersions into 3-dimensional homogeneous manifolds. Comment. Math. Helv. 82(1), 87–131 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  6. Eschenburg J.H., Tribuzy R.: Existence and uniqueness of maps into affine homogeneous spaces. Rend. Sem. Mat. Univ. Padova 69, 11–18 (1993)

    MathSciNet  MATH  Google Scholar 

  7. Kowalczyk D.: Isometric immersions into products of space forms. Geom. Dedicata 151, 1–8 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  8. Lira J.H., Tojeiro R., Vitório F.: A Bonnet theorem for isometric immersions into products of space forms. Arch. der Math. 95, 469–479 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  9. Petersen, P.: Riemannian geometry. In: Graduate Texts in Mathematics, vol. 171, 2nd edn, pp. xvi+401. Springer, New York (2006). ISBN: 978-0387-29246-5; 0-387-29246-2

  10. Spivak, M.: A Comprehensive Introduction to Differential Geometry, vol. III, 2nd edn, pp. viii+661. Publish or Perish, Inc., Wilmington (1979). ISBN: 0-914098-83-7

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Correspondence to Carlos do Rei Filho.

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C. do Rei Filho was partially supported by CAPES-Brazil.

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do Rei Filho, C., Vitório, F. A Bonnet Theorem for Submanifolds into Rotational Hypersurfaces. Results Math 71, 283–294 (2017). https://doi.org/10.1007/s00025-016-0550-y

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  • DOI: https://doi.org/10.1007/s00025-016-0550-y

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