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ON BI-HARMONIC HYPERSURFACES IN EUCLIDEAN SPACE OF ARBITRARY DIMENSION

Part of: Global differential geometry Symplectic geometry, contact geometry

Published online by Cambridge University Press:  18 December 2014

RAM SHANKAR GUPTA
RAM SHANKAR GUPTA*
Affiliation:
University School of Basic and Applied Sciences, Guru Gobind Singh Indraprastha University, Sector-16C, Dwarka, New Delhi-110078, India E-mail: ramshankar.gupta@gmail.com
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Abstract

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The following Chen's bi-harmonic conjecture made in 1991 is well-known and stays open: The only bi-harmonic submanifolds of Euclidean spaces are the minimal ones. In this paper, we prove that the bi-harmonic conjecture is true for bi-harmonic hypersurfaces with three distinct principal curvatures of a Euclidean space of arbitrary dimension.

MSC classification

Primary: 53D12: Lagrangian submanifolds; Maslov index
Secondary: 53C40: Global submanifolds 53C42: Immersions (minimal, prescribed curvature, tight, etc.)
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 57 , Issue 3 , September 2015 , pp. 633 - 642
Copyright
Copyright © Glasgow Mathematical Journal Trust 2014 

References

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