The high-velocity water maser sources at the center
of NGC4258 provide the compelling evidence for the presence of
a central supermassive black hole of a mass of 
(Miyoshi et al. 1995; Nakai et al. 1995).
Curiously, the position and velocity distribution of these maser sources
are fitted well with a warped Keplerian disk model
in which the inner and outer radii of the emitting region
are 0.12pc and 0.26pc, respectively
(Miyoshi et al. 1995; Nakai et al. 1995).
The maser disk is so thin that the upper limit of the disk thickness
is 
pc (Moran et al. 1995).
Such a disk can be perturbed by global one-armed (m=1) oscillations (e.g., Kato 1983). The purpose of this paper is to examine the characteristics of one-armed warping modes supposed to be present in the maser disk of NGC4258.
As an unperturbed equilibrium disk, we take a non-self-gravitating, axisymmetric disk rotating around a black hole. To simulate the weak general relativistic effect, we use the pseudo-Newtonian potential (Paczynski & Wiita 1980). We assume that the gas obeys a polytropic relation with an index of 5/3, adopt a simple toy model for the density distribution shown by contours in Fig. 1(b), and consider a linear adiabatic perturbation. As the boundary conditions for the resulting second-order partial differential equation for the perturbation, we require that the Lagrangian enthalpy perturbation vanishes at the disk surface, and that the Eulerian enthalpy perturbation is antisymmetric with respect to z.
In Fig. 1, we present a typical example of
a fundamental warping mode:
(a) the 
-distribution of the vertically-averaged
perturbed quantities and
(b) the 
-distribution of perturbed quantities.
The preiod of the mode is 
.
From Fig. 1
we notice that
the structure of the fundamental warping mode is in agreement with
the observed spatial distribution of the maser spots
of NGC4258.
Moreover, we find that the velocity vector
associated with the warping mode is roughly parallel to the z-axis,
especially near the equatorial plane.
This feature is also consistent with the observed nearly-Keplerian
velocity distribution of maser spots of NGC4258.
Figure 1: Structure of the fundamental warping mode:
(a) the 
-distribution of the perturbed quantities
averaged vertically over the half-thickness of the disk
and (b) the 
-distribution of the perturbed quantities.
A gray-scale representation denotes
the distribution of the enthalpy perturbation.
Arrows superposed on the gray-scale plot are
the perturbed velocity vectors in the maser emitting region
(surrounded by dashed lines).
Note that the enthalpy perturbation and the azimuthal component
of velocity perturbation vary
as 
, while the poloidal components of
velocity perturbation vary as 
,
where 
is the phase of the perturbation.
Contours in Fig. 1(b),
which show the unperturbed density distribution,
are separated by 0.1