Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Lagrangian angle and the K\"ahler angle of immersed surfaces in
  the complex plane $\bbc^2$   In this paper, we discuss the Lagrangian angle and the K\"ahler angle of
immersed surfaces in $\mathbb C^2$. Firstly, we provide an extension of
Lagrangian angle, Maslov form and Maslov class to more general surfaces in
$\mathbb C^2$ than Lagrangian surfaces, and then naturally extend a theorem by
J.-M. Morvan to surfaces of constant K\"ahler angle, together with an
application showing that the Maslov class of a compact self-shrinker surface
with constant K\"ahler angle is generally non-vanishing. Secondly, we obtain
two pinching results for the K\"ahler angle which imply rigidity theorems of
self-shrinkers with K\"ahler angle under the condition that $\int_M
|h|^2e^{-\frac{|x|^2}{2}}dV_M<\infty$, where $h$ and $x$ denote, respectively,
the second fundamental form and the position vector of the surface.

12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: nlin
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The categories of this paper are: hep-th