  In supernova cores and neutron star crusts, nuclei are thought to deform to
rodlike and slablike shapes, which are often called nuclear pasta. We study the
equilibrium properties of the nuclear pasta by using a liquid drop model with
curvature corrections. It is confirmed that the curvature effect acts to lower
the transition densities between different shapes. We also examine the gyroid
structure, which was recently suggested as a different type of nuclear pasta by
analogy with the polymer systems. The gyroid structure investigated in this
paper is approximately formulated as an extension of the periodic minimal
surface whose mean curvature vanishes. In contrast to our expectations, we find
from the present approximate formulation that the curvature corrections act to
slightly disfavor the appearance of the gyroid structure. By comparing the
energy corrections in the gyroid phase and the hypothetical phases composed of
d-dimensional spheres, where d is a general dimensionality, we show that the
gyroid is unlikely to belong to a family of the generalized dimensional
spheres.
