Abstract
In this paper, we prove a version of the fundamental theorem of submanifolds to target manifolds with warped structure.
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Bonnet, O.: Mémorie sur la théorie des surfaces applicables sur une surface donnée. J. École Polytech. 42 (1867)
Chen Q., Xiang C.R.: Isometric immersions into warped product spaces. Acta Math. Sin. Engl. Ser. 26(12), 2269–2282 (2010)
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
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)
Daniel B.: Isometric immersions into 3-dimensional homogeneous manifolds. Comment. Math. Helv. 82(1), 87–131 (2007)
Eschenburg J.H., Tribuzy R.: Existence and uniqueness of maps into affine homogeneous spaces. Rend. Sem. Mat. Univ. Padova 69, 11–18 (1993)
Kowalczyk D.: Isometric immersions into products of space forms. Geom. Dedicata 151, 1–8 (2011)
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)
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
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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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