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A DDVV INEQUALITY FOR SUBMANIFOLDS OF WARPED PRODUCTS

Part of: Global differential geometry

Published online by Cambridge University Press:  05 January 2017

JULIEN ROTH
JULIEN ROTH*
Affiliation:
LAMA, UPEM-UPEC-CNRS, Cité Descartes, Champs sur Marne, 77454 Marne-la-Vallée cedex 2, France email julien.roth@u-pem.fr
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Abstract

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We prove a DDVV inequality for submanifolds of warped products of the form $I\times _{a}\mathbb{M}^{n}(c)$ , where $I$ is an interval and $\mathbb{M}^{n}(c)$ is a real space form of curvature $c$ . As an application, we give a rigidity result for submanifolds of $\mathbb{R}\times _{e^{\unicode[STIX]{x1D706}t}}\mathbb{H}^{n}(c)$ .

Keywords

warped productrigidityimmersion

MSC classification

Primary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.)
Secondary: 53C24: Rigidity results
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 95 , Issue 3 , June 2017 , pp. 495 - 499
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

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