In the book on Ricci flow by Andrews and Hopper, it has been proved that if Ricci flow on $M$ has a finite time singularity at time $T$ then $\lim_{t \nearrow T} \sup_{x\in M} |Rm(x,t)|=\infty$. I am wondering whether the following assertions are false or unknown (I know that the following assertions are true if $\lim$ is replaced by $\lim \sup$):
- $\lim_{t \nearrow T} \sup_{x\in M} |Ric(x,t)|=\infty$
- $\lim_{t \nearrow T} \sup_{x\in M} |R(x,t)|=\infty$ when $M$ is K\"{a}hler.
Thanks in advance.