Abstract
Abstract
The present work is devoted to investigate anisotropic conformal transformation of conic pseudo-Finsler surfaces (M, F), that is,
F
(
x
,
y
)
⟼
F
―
(
x
,
y
)
=
e
ϕ
(
x
,
y
)
F
(
x
,
y
)
, where the function
ϕ
(
x
,
y
)
depends on both position x and direction y, contrary to the ordinary (isotropic) conformal transformation which depends on position only. If F is a pseudo-Finsler metric, the above transformation does not yield necessarily a pseudo-Finsler metric. Consequently, we find out necessary and sufficient condition for a (conic) pseudo-Finsler surface (M, F) to be transformed to a (conic) pseudo-Finsler surface
(
M
,
F
―
)
under the transformation
F
―
=
e
ϕ
(
x
,
y
)
F
. In general dimension, it is extremely difficult to find the anisotropic conformal change of the inverse metric tensor in a tensorial form. However, by using the modified Berwald frame on a Finsler surface, we obtain the change of the components of the inverse metric tensor in a tensorial form. This progress enables us to study the transformation of the Finslerian geometric objects and the geometric properties associated with the transformed Finsler function
F
―
. In contrast to isotropic conformal transformation, we have a non-homothetic conformal factor
ϕ
(
x
,
y
)
that preserves the geodesic spray. Also, we find out some invariant geometric objects under the anisotropic conformal change. Furthermore, we investigate a sufficient condition for
F
―
to be dually flat or/and projectively flat. Finally, we study some special cases of the conformal factor
ϕ
(
x
,
y
)
. Various examples are provided whenever the situation needs.