Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The extrinsic holonomy Lie algebra of a parallel submanifold   We investigate parallel submanifolds of a Riemannian symmetric space $N$. The
special case of a symmetric submanifold has been investigated by many authors
before and is well understood. We observe that there is an intrinsic property
of the second fundamental form which distinguishes full symmetric submanifolds
from arbitrary full parallel submanifolds of $N$, usually called "1-fullness of
$M$". Furthermore, for every parallel submanifold $M$ of $N$ we consider the
pullback bundle $TN|M$ with its induced connection, which admits a
distinguished parallel subbundle $osc M$, usually called the "second osculating
bundle of $M$". If $M$ is a complete parallel submanifold of $N$, then we can
describe the corresponding holonomy Lie algebra of $osc M$ by means of the
second fundamental form of $M$ and the curvature tensor of $N$ at the origin.
If moreover $N$ is simply connected and $M$ is even a full symmetric
submanifold of $N$, then we will calculate the holonomy Lie algebra of $TN|M$
in an explicit form.

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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: cs
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The categories of this paper are: hep-th
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The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc