Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Semi-isometric CR immersions of CR manifolds into K\"ahler manifolds and
  applications   We study the second fundamental form of semi-isometric CR immersions from
strictly pseudoconvex CR manifolds into K\"ahler manifolds. As an application,
we give a precise condition for the CR umbilicality of real hypersurfaces,
extending an well-known theorem by Webster on the nonexistence of CR umbilical
points on generic real ellipsoids. As other applications, we extend the
linearity theorem of Ji-Yuan for CR immersions into spheres with vanishing
second fundamental form to the important case of three-dimensional manifolds,
and prove the ``first gap'' theorem in the spirit of Webster, Faran,
Cima-Suffridge, and Huang for semi-isometric CR immersions into a complex
euclidean space of ``low'' codimension. Our new approach to the linearity
theorem is based on the study of the first positive eigenvalue of the Kohn
Laplacian.

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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci