Riv.Mat.Univ.Parma (7) 2 (2003)


Subelliptic F-harmonic maps

Pages: 33-50
Received: 9 December 2002   
Mathematics Subject Classification (2000): 58E20 - 53C43 - 32V20 - 35H20

Abstract: Owing to the ideas of M. Ara (cf. [1]) and K. Uhlenback (cf. [16]) we consider F-pseudoharmonic maps, i.e. critical points of the energy EF ( Φ) = ∫ F ( 1/2 traceH Φ*h )θ ∧(dθ)n, on the class of smooth maps Φ : M --> N from a (compact) strictly pseudoconvex CR manifold ( M, q) to a Riemannian manifold (N,h), where q is a contact form and F : ( o, ∞) --> (o, ∞) is a C2 function such that F'(t) > 0. F-pseudoharmonic maps generalize both J. Jost & C-J. Xu's subelliptic harmonic maps (the case F(t) = t, cf. [12]) and P. Hajlasz & P. Strzelecki's subelliptic p-harmonic maps (the case F(t) = (2t)p/2, cf. [9]). We obtain the first variation formula for EF( f). We investigate the relationship between F-pseudoharmonicity and pseudoharmonicity, by exploiting the analogy between CR and conformal geometry (cf. [1] for the Riemannian counterpart). We consider {\em pseudoharmonic morphisms} from a strictly pseudoconvex CR manifold and show that any pseudoharmonic morphism is a pseudoharmonic map (the CR analogue of T. Ishihara's theorem, cf. [11]). We give a geometric interpretation of F-pseudoharmonicity in terms of the Fefferman metric of (M, q).

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