Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Splitting submanifolds in rational homogeneous spaces of Picard number
  one   Let $M$ be a complex manifold. We prove that a compact submanifold $S\subset
M$ with splitting tangent sequence (called a splitting submanifold) is rational
homogeneous when $M$ is in a large class of rational homogeneous spaces of
Picard number one. Moreover, when $M$ is irreducible Hermitian symmetric, we
prove that $S$ must be also Hermitian symmetric. The basic tool we use is the
restriction and projection map $\pi$ of the global holomorphic vector fields on
the ambient space which is induced from the splitting condition. The usage of
global holomorphic vector fields may help us set up a new scheme to classify
the splitting submanifolds in explicit examples, as an example we give a
differential geometric proof for the classification of compact splitting
submanifolds with $\dim\geq 2$ in a hyperquadric, which has been previously
proven using algebraic geometry.

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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: nlin
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The categories of this paper are: math-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an