Semi-isometric CR immersions of CR manifolds into Kähler manifolds and applications
نویسندگان
چکیده
We study the second fundamental form of semi-isometric CR immersions from strictly pseudoconvex manifolds into K\"ahler manifolds. As an application, we give a precise condition for umbilicality real hypersurfaces, extending well-known theorem by Webster on nonexistence umbilical points generic ellipsoids. other applications, extend linearity Ji-Yuan spheres with vanishing to important case three-dimensional manifolds, and prove ``first gap'' in spirit Webster, Faran, Cima-Suffridge, Huang complex euclidean space ``low'' codimension. Our new approach is based first positive eigenvalue Kohn Laplacian.
منابع مشابه
Isometric Immersions into 3-dimensional Homogeneous Manifolds
We give a necessary and sufficient condition for a 2-dimensional Riemannian manifold to be locally isometrically immersed into a 3-dimensional homogeneous manifold with a 4-dimensional isometry group. The condition is expressed in terms of the metric, the second fundamental form, and data arising from an ambient Killing field. This class of 3-manifolds includes in particular the Berger spheres,...
متن کاملThe Modified Calabi-yau Problems for Cr-manifolds and Applications
In this paper, we derive a partial result related to a question of Yau: “Does a simply-connected complete Kähler manifold M with negative sectional curvature admit a bounded non-constant holomorphic function?” Main Theorem. Let M be a simply-connected complete Kähler manifold M with negative sectional curvature ≤ −1 and S∞(M) be the sphere at infinity of M. Then there is an explicit bounded con...
متن کاملComplex cobordism and embeddability of CR-manifolds
This paper studies complex cobordisms between compact, three dimensional, strictly pseudoconvex Cauchy-Riemann manifolds. Suppose the complex cobordism is given by a complex 2-manifold X with one pseudoconvex and one pseudoconcave end. We answer the following questions. To what extent is X determined by the pseudoconvex end? What is the relation between the embeddability of the pseudoconvex end...
متن کاملAutomorphism Groups of Normal Cr 3-manifolds
We classify the normal CR structures on S and their automorphism groups. Together with [2], this closes the classification of normal CR structures on contact 3-manifolds. We give a criterion to compare 2 normal CR structures, and we show that the underlying contact structure is, up to diffeomorphism, unique.
متن کاملOn Spherical CR Uniformization of 3-Manifolds
We consider the discrete representations of 3-manifold groups into PU(2, 1) that appear in the Falbel-Koseleff-Rouillier, such that the peripheral subgroups have cyclic unipotent holonomy. We show that two of these representations have conjugate images, even though they represent different 3-manifold groups. This illustrates the fact that a discrete representation π1(M) → PU(2, 1) with cyclic u...
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: Annali della Scuola normale superiore di Pisa. Classe di scienze
سال: 2021
ISSN: ['0391-173X', '2036-2145']
DOI: https://doi.org/10.2422/2036-2145.201902_008