Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Projectively invariant objects and the index of the group of affine
  transformations in the group of projective transformations   The paper is grown from the lecture course "Metric projective geometry" which
I hold at the summer school "Finsler geometry with applications" at Karlovassi,
Samos, in 2014, and at the workshop before the 8th seminar on Geometry and
Topology of the Iranian Mathematical society at the Amirkabir University of
Technology in 2015. The goal of this lecture course was to show how effective
projectively invariant objects can be used to solve natural and named problems
in differential geometry, and this paper also does it: I give easy new proofs
to many known statements, and also prove the following new statement: on a
complete Riemannian manifold of nonconstant curvature the index of the group of
affine transformations in the group of projective transformations is at most
two.

32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex