Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Elliptic Curves, Algebraic Geometry Approach in Gravity Theory and Some
  Applications in Theories with Extra Dimensions I   Motivated by the necessity to find exact solutions with the elliptic
Weierstrass function of the Einstein's equations (see gr-qc/0105022),the
present paper develops further the proposed approach in hep-th/0107231,
concerning the s.c. cubic algebraic equation for effective parametrization.
Obtaining an ''embedded'' sequence of cubic equations, it is shown that it is
possible to parametrize also a multi-variable cubic curve, which is not the
standardly known case from algebraic geometry. Algebraic solutions for the
contravariant metric tensor components are derived and the parametrization is
extended in respect to the covariant components as well. It has been speculated
that corrections to the extradimensional volume in theories with extra
dimensions should be taken into account, due to the non-euclidean nature of the
Lobachevsky space. It was shown that the mechanism of exponential "damping" of
the physical mass in the higher-dimensional brane theory may be more
complicated due to the variety of contravariant metric components for a
spacetime with a given constant curvature. The invariance of the low-energy
type I string theory effective action is considered in respect not only to the
known procedure of compactification to a four-dimensional spacetime, but also
in respect to rescaling the contravariant metric components. As a result,
instead of the simple algebraic relations between the parameters in the string
action, quasilinear differential equations in partial derivatives are obtained,
which have been solved for the most simple case. In the Appendix, a new block
structure method is presented for solving the well known system of operator
equations in gravity theory in the N-dimensional case.

21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga