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Subelliptic Biharmonic Maps

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Abstract

We study subelliptic biharmonic maps, i.e., smooth maps ϕ:M→N from a compact strictly pseudoconvex CR manifold M into a Riemannian manifold N which are critical points of the energy functional \(E_{2,b} (\phi ) = \frac{1}{2} \int_{M} \| \tau_{b} (\phi ) \|^{2} \theta \wedge (d \theta)^{n}\). We show that ϕ:M→N is a subelliptic biharmonic map if and only if its vertical lift ϕ∘π:C(M)→N to the (total space of the) canonical circle bundle \(S^{1} \to C(M) \stackrel{\pi}{\longrightarrow} M\) is a biharmonic map with respect to the Fefferman metric F θ on C(M).

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università degli Studi della Basilicata, Contrada Macchia Romana, 85100, Potenza, Italy

    Sorin Dragomir

  2. Dipartimento di Matematica e Informatica, Università degli Studi di Cagliari, Via Ospedale 72, 09124, Cagliari, Italy

    Stefano Montaldo

Authors
  1. Sorin Dragomir
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  2. Stefano Montaldo
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Correspondence to Sorin Dragomir.

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Communicated by Alexander Isaev.

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Dragomir, S., Montaldo, S. Subelliptic Biharmonic Maps. J Geom Anal 24, 223–245 (2014). https://doi.org/10.1007/s12220-012-9335-z

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  • DOI: https://doi.org/10.1007/s12220-012-9335-z

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