D1 and D5-brane giant gravitons on $Ad{S}_3\times S^3\times S^3\times S^1$

We construct various examples of 1/4-BPS giant gravitons embedded into the type IIB supergravity background $AdS_{3} \times S^{3}{+} \times S^{3}{-} \times S^{1}$withpureR-Rflux:twoD1-branegiantswrapping1-cyclesin$AdS_{3}$and$S^{3}{+} \times S^{3}{-}$, and one D5-brane giant wrapping a 4-cycle in $S_{+}^3\times S_{-}^3$ and the $S^1$. These D-branes are supported by angular momenta $\alpha$ P on one 3-sphere and $(1-\alpha )$ P on the other. We then construct a general class of 1/8-BPS D5-brane giant gravitons wrapping 4-cycles $\mathrm{\Sigma }$ in $S_{+}^3\times S_{-}^3$ and the $S^1$. Here $\mathrm{\Sigma }$ is the intersection of a holomorphic surface $\mathcal{C}$ in ${\mathbb{C}}_{+}^2\times {\mathbb{C}}_{-}^2$ with the $S_{+}^3\times S_{-}^3$ submanifold. The holomorphic surface $\mathcal{C}$ is defined by $f(y_1{z}_1,y_1{z}_2,y_2{z}_1,y_2{z}_2)=0$, with $y_a$ and $z_a$ the ${\mathbb{C}}_{\pm }^2$ complex coordinates. There is supersymmetry enhancement to 1/4-BPS in the special case $f(y_1{z}_1)=0$ of which our original D5-brane giant graviton is an example.