Abstract
In this chapter we discuss two other useful ways of constructing immersions of product manifolds from immersions of the factors, with an increasing degree of generality. Namely, we introduce the notions of (extrinsic) warped products of immersions and, more generally, of partial tubes over extrinsic products of immersions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Berndt, J., Console, S., Olmos, C.: Submanifolds and Holonomy, 2nd edn. Research Notes in Mathematics. Chapman and Hall/CRC, Boca Raton (2016)
Carter, S., Dursun, U.: Partial tubes and Chen submanifolds. J. Geom. 63, 30–38 (1998)
Carter, S., West, A.: Partial tubes about immersed manifolds. Geom. Dedicata 54, 145–169 (1995)
Chen, B.-Y.: On isometric minimal immersions from warped products into real space forms. Proc. Edinb. Math. Soc. 45, 579–587 (2002)
Dajczer, M., Tojeiro, R.: Isometric immersions in codimension two of warped products into space forms. Ill. J. Math. 48, 711–746 (2004)
Dajczer, M., Vlachos, Th.: Isometric immersions of warped products. Proc. Am. Math. Soc. 141, 1795–1803 (2013)
do Carmo, M., Dajczer, M.: Rotation hypersurfaces in spaces of constant curvature. Trans. Am. Math. Soc. 277, 685–709 (1983)
Hiepko, S.: Eine innere Kennzeichnung der verzerrten Produkte. Math. Ann. 241, 209–215 (1979)
Heintze, E., Olmos, C., Thorbergsson, G.: Submanifolds with constant principal curvatures and normal holonomy groups. Int. J. Math. 2, 167–175 (1991)
Nölker, S.: Isometric immersions of warped products. Differ. Geom. Appl. 6, 1–30 (1996)
Tojeiro, R.: A decomposition theorem for immersions of product manifolds. Proc. Edinb. Math. Soc. 59, 247–269 (2016)
Tojeiro, R.: Conformal immersions of warped products. Geom. Dedicata 128, 17–31 (2007)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Science+Business Media, LLC, part of Springer Nature
About this chapter
Cite this chapter
Dajczer, M., Tojeiro, R. (2019). Isometric Immersions of Warped Products. In: Submanifold Theory . Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-9644-5_10
Download citation
DOI: https://doi.org/10.1007/978-1-4939-9644-5_10
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4939-9642-1
Online ISBN: 978-1-4939-9644-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)