Hi there! Here is a piece from a book about general relativity http://www.photodump.com/direct/Bbki...ormulation.jpg and it is imposible for me to get equation (1) or to get (3) from (2). Does anyone have any idea what to do? I get (1) only assuming that we care only for a spacelike variation of V, so I project the lie derivative of V with respect to K , to the spacelike hypersyrface via the projective tensor δab+VaVb where the a index is contravariant and the b index covariant. I need some help. Thanks.