Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Austere Submanifolds of Dimension Four: Examples and Maximal Types   Austere submanifolds in Euclidean space were introduced by Harvey and Lawson
in connection with their study of calibrated geometries. The algebraic
possibilities for second fundamental forms of 4-dimensional austere
submanifolds were classified by Bryant, into three types which we label A, B,
and C. In this paper, we show that type A submanifolds correspond exactly to
real Kahler submanifolds, we construct new examples of such submanifolds in R^6
and R^10, and we obtain classification results on submanifolds of types B and C
with maximal second fundamental forms.

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The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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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: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th