Kodai Mathematical Journal

On p-biharmonic submanifolds in nonpositively curved manifolds

Xiangzhi Cao and Yong Luo

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Abstract

Let u: (M, g) → (N, h) be a map between Riemannian manifolds (M, g) and (N, h). The p-bienergy of u is τp(u) = ∫M|τ(u)|p g, where τ(u) is the tension field of u and p > 1. Critical points of τp are called p-biharmonic maps and isometric p-biharmonic maps are called p-biharmonic submanifolds. When p = 2, p-biharmonic submanifolds are biharmonic submanifolds and in recent years many nonexistence results are found for biharmonic submanifolds in nonpositively curved manifolds. In this paper we will study the nonexistence result for general p-biharmonic submanifolds.

Article information

Source
Kodai Math. J., Volume 39, Number 3 (2016), 567-578.

Dates
First available in Project Euclid: 2 November 2016

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1478073773

Digital Object Identifier
doi:10.2996/kmj/1478073773

Mathematical Reviews number (MathSciNet)
MR3567234

Zentralblatt MATH identifier
1355.53015

Citation

Cao, Xiangzhi; Luo, Yong. On p -biharmonic submanifolds in nonpositively curved manifolds. Kodai Math. J. 39 (2016), no. 3, 567--578. doi:10.2996/kmj/1478073773. https://projecteuclid.org/euclid.kmj/1478073773


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