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

**ELISABETTA BARLETTA**

*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
*E*_{F} ( Φ) = ∫ F ( 1/2 trace_{Gθ} (π_{H} 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 C^{2} 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 E_{F}( 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).

Home Riv.Mat.Univ.Parma