D = 11 dS ₅ backgrounds with enhanced supersymmetry

We classify all warped $dS_5$ backgrounds in $D=11$ supergravity with enhanced supersymmetry. show that preserving $N=16$ supersymmetries consist of either a stack M5 branes transverse space $\mathbb{R}^5$, or generalized M5-brane configuration $\mathbb{R} \times N_4$, where $N_4$ is hyper-Kahler manifold and the $M5$-brane harmonic function determined by potential on $N_4$. Moreover, we find there are no exactly $N=24$ supersymmetries. Backgrounds $N=32$ correspond to $\mathbb{R}^{1,10}$ $AdS_7\times S^4$.