An Obata-type theorem in CR geometry
نویسندگان
چکیده
منابع مشابه
An Obata-type Theorem in Cr Geometry
We discuss a sharp lower bound for the first positive eigenvalue of the sublaplacian on a closed, strictly pseudoconvex pseudohermitian manifold of dimension 2m + 1 ≥ 5. We prove that the equality holds iff the manifold is equivalent to the CR sphere up to a scaling. For this purpose, we establish an Obata-type theorem in CR geometry which characterizes the CR sphere in terms of a nonzero funct...
متن کاملAn Obata-type Theorem on a Three-dimensional Cr Manifold
We prove a CR version of the Obata’s result for the first eigenvalue of the sub-Laplacian in the setting of a compact strictly pseudoconvex pseudohermitian three dimensional manifold with non-negative CR-Paneitz operator which satisfies a Lichnerowicz type condition. We show that if the first positive eigenvalue of the sub-Laplacian takes the smallest possible value then, up to a homothety of t...
متن کاملOn the CR–Obata theorem and some extremal problems associated to pseudo scalar curvature on the real ellipsoids in C
where (hαβ) is the positive definite n × n matrix on M , which is uniquely determined by the Levi form Lθ(u, v) = −idθ(u, v) for u, v ∈ H(M). Let ∆sb be the sub-Laplacian with respect to θ (see [8], [22] and [7] for references) and let μ1 be the first positive eigenvalue of ∆sb on (M, θ). Let Rαβ be the Webster pseudo Ricci curvature, R be the pseudo scalar curvature and Tor be the pseudo torsi...
متن کاملDegeneracy Loci in CR Geometry
Starting on the next page is the 16-page Chapter II excerpted from my dissertation, “Enumeration and Normal Forms for Singularities in CauchyRiemann Structures,” 1997, University of Chicago. I have made a few minor editorial modifications so that Chapter II can be read without referring to the other Chapters. Section 5 of Chapter II is a summary of results appearing in my unpublished lecture no...
متن کاملTractor Bundles in Cr Geometry
This is an outline of my lecture at the Hayama Symposium on several complex variables on December 21, 2002. The subject of the talk are new applications of the canonical Cartan connection for CR manifolds. Most of the results I will report on are based on joint research (partly in progress) with A.R. Gover and with J. Slovák and V. Souček. Partly, these results are specific for the class of CR ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 2013
ISSN: 0022-040X
DOI: 10.4310/jdg/1381931736