Kodai Mathematical Journal

On p-biharmonic submanifolds in nonpositively curved manifolds

Xiangzhi Cao and Yong Luo

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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.

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

First available in Project Euclid: 2 November 2016

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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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