Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 60, Number 2 (2008), 363-396.
Minimality in CR geometry and the CR Yamabe problem on CR manifolds with boundary
We study the minimality of an isometric immersion of a Riemannian manifold into a strictly pseudoconvex CR manifold endowed with the Webster metric hence consider a version of the CR Yamabe problem for CR manifolds with boundary. This occurs as the Yamabe problem for the Fefferman metric (a Lorentzian metric associated to a choice of contact structure on , ) on the total space of the canonical circle bundle (a manifold with boundary and is shown to be a nonlinear subelliptic problem of variational origin. For any real surface we show that the mean curvature vector of is expressed by provided that is tangent to the characteristic direction of , thus demonstrating the relationship between the classical theory of submanifolds in Riemannian manifolds (cf. e.g.) and the newer investigations in , ,  and . Given an isometric immersion of a Riemannian manifold into the Heisenberg group we show that hence start a Weierstrass representation theory for minimal surfaces in .
J. Math. Soc. Japan Volume 60, Number 2 (2008), 363-396.
First available in Project Euclid: 30 May 2008
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 53C40: Global submanifolds [See also 53B25]
Secondary: 32V20: Analysis on CR manifolds 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]
DRAGOMIR, Sorin. Minimality in CR geometry and the CR Yamabe problem on CR manifolds with boundary. J. Math. Soc. Japan 60 (2008), no. 2, 363--396. doi:10.2969/jmsj/06020363. https://projecteuclid.org/euclid.jmsj/1212156655