AN OBATA-TYPE THEOREM ON A THREE-DIMENSIONAL CR MANIFOLD
نویسندگان
چکیده
منابع مشابه
An 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 کاملAn 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 Result for the First Eigenvalue of the Sub-laplacian on a Cr Manifold with a Divergence-free Torsion
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 manifold which satisfies a Lichnerowicz type condition and has a divergence free pseudohermitian torsion. We show that if the first positive eigenvalue of the sub-Laplacian takes the smallest possible value then, up to a homothety of the pse...
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 کاملOn CR-Lightlike Product of an Indefinite Kaehler Manifold
The geometry of CR-submanifolds of Kaehler manifolds was initiated by Bejancu 1 and has been developed by 2–5 and others. They studied the geometry of CR-submanifolds with positive definite metric. Thus, this geometry may not be applicable to the other branches of mathematics and physics, where the metric is not necessarily definite. Moreover, because of growing importance of lightlike submanif...
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: Glasgow Mathematical Journal
سال: 2013
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089513000256