In this paper, we study conformal mapping between O- spaces. We
find The existing of the necessary and sufficient conditions for a
conformal mapping .
We prove that there is no nontrivial conformal mapping between Ospaces
with the same structure.
The main objective of this research is to develop an
arithmetic model for transformations between geographic and
State Plane Coordinate within the three types of Conformal
Syrian Conical projection (tangent, secant and Semiconformal),
In order to
enable all Specialists and surveyors to
carry out direct and reverse transformations of horizontal
coordinates of the points without returning to any competent
authorities to avoid any administrative and computational
complexities.
In this paper we study conformal mappings between
special Parabolically Kahlerian Spaces (commutative spaces).
A proved , if exist conformal mapping between commutative
Kahlerin spaces ,then the mapping is Homothetic
mapping,
in this paper we:
1) defined Riemannian space , conformal mapping, Einstein
space , Ricci recurrent Einstein space.
2) study conformal mapping between Einstein spaces
corresponding flat surface, and Ricci recurrent Einstein
space.
in this paper we:
defined Riemannian spaces, conformal mappings, Einstein
spaces, Riemannian symmetric spaces, Ricci spaces and
Ricci symmetric spaces, recall the fundamental properties of
these spaces
The transformation of coordinates between the global coordinate system yield
ellipsoid WGS84 (World Geodetic System 1984) and the local coordinate system yield
ellipsoid Clark1880 in different regions of Syria, is the essential step in the effectiv
e use of
GNSS (Global Navigation Satellite Systems) surveying techniques in Syria, and the
transformation occurs with 3D transformation between one ellipsoid and another, or 2D
transformation directly between two planar. The transformation must be understood,
analyzed and tested. The research is about the accuracy of the 2D transformation in small
area to give coordinates can be directly used in different surveying and engineering works,
and about studying the common points number and their distribution effect on
transformation accuracy, and conclude that the biggest effect on transformation accuracy is
for the common points distribution.
We define Riemann – Banach space and the space conformal to
the Euclidean planer space, then we create The necessary and
sufficient conditions in order to be Riemann – Banach
space conformal to the Euclidean space, then we prove that
constant- curvature Riemann – Banach spaces which have
are conformal to the Euclidean space. Finally,
we create locally, the measurement in constant curvature
Riemann –Banach spaces.
