I should prefer there to be no discussion of my private affairs.我宁愿不要讨论我的私事。
People don’t want there to be another war.人们不希望再有战争了。
另外，作介词宾语时，如果是介词for，只能用“there to be”其它介词用“there being”
The teacher was waiting for there to be complete silence.老师在等着大家都安静下来。
I never dreamed of there being any good chance for me.我做梦也没想到我会有好机会。

3. 作状语的there be 形式，通常用“there being”结构。
There being nothing else to do ,we went home.因为没有其他事可做，我们就回家了。
They closed the door ,there being no customers.因为没有顾客，他们的店关门了。