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We construct some new dynamical $p$-brane solutions to gravity theories oncurved backgrounds. We discuss the relations between dynamical branes, a newtime-dependent solution on complex projective space $\mathbb{C}{\rm P}^n$ andthe static $p$-branes on the orbifold ${\mathbb C}^n/{\mathbb Z}_n$.

Dynamical branes on expanding orbifold and complex projective space