Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Schwarzian Curvature   We start with introducing one of the most fundamental notions of differential
geometry, Manifolds. We present some properties and constructions such as
submanifolds, tangent spaces and the tangent map. Then we continue with
introducing the real and complex projective space, and describe them from some
different points of view. This part is finished by showing that CP^n is a
Grassmannian manifold. At this stage we are ready to present the main subject
of this thesis. The Schwarzian curvature, usually seems to be an accidental
by-product of the calculations, can be seen as a geometric interpretation of
the Schwarzian derivative. Flanders interpreted the Schwarzian derivative of a
C''' function as a curvature for curves in the projective line by using the
moving frame method of Cartan. The same argumentation was extended by Gao to
obtain the Schwarzian curvatures for curves in higher dimensional projective
spaces. I give detailed presentation of Gao's work, where he presented the
general formulas for the Schwarzian curvatures for curves in CP^n and gives
some properties for the behaviour of the formulas, for example the
transformation rules under change of coordinates. The Schwarzian curvatures for
curves in CP, CP^2 and CP^3 are calculated, and some examples are given.

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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: astro-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: stat