  On the basis of the Bogoliubov-de Gennes theory for the two-dimensional
extended Hubbard model, the vortex structure in d-wave superconductors is
investigated including the contribution of the induced incommensurate
antiferromagnetism around the vortex core. As the on-site repulsive interaction
$U$ increases, the spatial structure of charge and spin changes from the
antiferromagnetic state with checkerboard modulation to that with the stripe
modulation. By the effect of the induced antiferromagnetic moment, the
zero-energy density of states is suppressed, and the vortex core radius
increases. We also study the effect of the local density of states (LDOS)
change on the site-dependent nuclear relaxation rate $T_1^{-1}({\bf r})$. These
results are compared with a variety of experiments performed on high $T_c$
cuprates.
