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WARPED PRODUCTS IN RIEMANNIAN MANIFOLDS

Part of: Global differential geometry

Published online by Cambridge University Press:  09 September 2014

KWANG-SOON PARK
KWANG-SOON PARK*
Affiliation:
Department of Mathematical Sciences, Seoul National University, Seoul 151-747, Republic of Korea email [email protected]
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Abstract

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In this paper we prove two inequalities relating the warping function to various curvature terms, for warped products isometrically immersed in Riemannian manifolds. This extends work by B. Y. Chen [‘On isometric minimal immersions from warped products into real space forms’, Proc. Edinb. Math. Soc. (2) 45(3) (2002), 579–587 and ‘Warped products in real space forms’, Rocky Mountain J. Math.34(2) (2004), 551–563] for the case of immersions into space forms. Finally, we give an application where the target manifold is the Clifford torus.

Keywords

warped productsquared mean curvaturewarping functionsecond fundamental form

MSC classification

Secondary: 53C40: Global submanifolds 53C42: Immersions (minimal, prescribed curvature, tight, etc.) 53C50: Lorentz manifolds, manifolds with indefinite metrics
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 90 , Issue 3 , December 2014 , pp. 510 - 520
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

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