例：He stood there,his hand raised.= He stood there,with his hand raise.

独立主格结构的分词的选择取决于名词和分词之间的关系.如果是主谓关系就用现在分词,如果是动宾关系就用过去分词.
在这两句话中,his hands和后面的动词都是动宾关系.所以要用过去分词来表示被动.
补充：1.名词/主格代词+现在分词
名词/主格代词与现在分词之间是主谓关系.如：
The girl staring at him(= As the girl stared at him),he didn't know what to say.
姑娘两眼望着他,他不知道说什么好.
Time permitting(= If time permits),we will go for an outing tomorrow.如果时间允许的话,我们明天去郊游.
2.名词/主格代词+过去分词
名词/主格代词与过去分词之间是动宾关系.
如：The problems solved(= As the problems were solved),the quality has been improved.
随着问题的解决,质量已经提高了.
Her glasses broken(= Because her glasses were broken),she couldn't see the words on the blackboard.由于眼镜摔坏了,她看不见黑板上的字.其实我觉得第一句话有问题...hand和raise是主谓关系，那He stood there, his hand raised.= He stood there, with his hand raise. 这两句我觉得都该用raising。。应该是with his hand raised请举起手来：Please raise your hand.而不是Please your hand raise.raise的动作执行者是sb, hand是raise的动作承受者。加油~