Minimality in CR geometry and the CR Yamabe problem on CR manifolds with boundary
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- Dragomir Sorin
- Università degli Studi della Basilicata, Dipartimento di Matematica e Informatica
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Description
We study the minimality of an isometric immersion of a Riemannian manifold into a strictly pseudoconvex CR manifold M 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 θ on M, [20]) on the total space of the canonical circle bundle S1 → C(M) $\stackrel{\pi}{\ ightarrow}$ M (a manifold with boundary ∂C(M) = π-1 (∂M)) and is shown to be a nonlinear subelliptic problem of variational origin. For any real surface N = { φ = 0 } ⊂ H1 we show that the mean curvature vector of N $\hookrightarrow$ H1 is expressed by H = - $\frac{1}{2}$ $\sum$j=12 Xj (|Xφ|-1 Xjφ)ξ provided that N is tangent to the characteristic direction T of (H1, θ0), thus demonstrating the relationship between the classical theory of submanifolds in Riemannian manifolds (cf. e.g. [7]) and the newer investigations in [1], [6], [8] and [16]. Given an isometric immersion Ψ:N → Hn of a Riemannian manifold into the Heisenberg group we show that ΔΨ = 2 JT⊥ hence start a Weierstrass representation theory for minimal surfaces in Hn.
Journal
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- Journal of the Mathematical Society of Japan
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Journal of the Mathematical Society of Japan 60 (2), 363-396, 2008
The Mathematical Society of Japan
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Details 詳細情報について
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- CRID
- 1390001205115138304
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- NII Article ID
- 10024331660
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- NII Book ID
- AA0070177X
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- ISSN
- 18811167
- 18812333
- 00255645
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- NDL BIB ID
- 9468077
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- Text Lang
- en
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- Data Source
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- JaLC
- NDL
- Crossref
- CiNii Articles
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- Abstract License Flag
- Disallowed