Learned by Reading
In Wikipedia:
The metric “g” is defined to be the real part of “h”: The form “g” is a symmetric bilinear form on “TM” C, the complexified tangent bundle.
(Parse)
(S1 (S (S (NP (DT The) (JJ metric) ('' '') (NNP g) ('' ''))
(VP (AUX is)
(VP (VBN defined)
(S (VP (TO to)
(VP (AUX be)
(NP (NP (DT the) (JJ real) (NN part))
(PP (IN of) (FRAG ('' '')
(NP (NNP h)) ('' ''))))
(: :)
(S (NP (DT The) (NN form) ('' '') (NNP g) ('' ''))
(VP (AUX is)
(NP (NP (DT a) (JJ symmetric) (NN bilinear) (NN form))
(PP (IN on) ('' '')
(NP (NP (NNP TM) ('' '') (NNP C)) (, ,)
(NP (DT the) (JJ complexified) (NN tangent) (NN bundle))))
(. .)))
In Wikipedia:
In mathematics, the Killing form ’”, named after Wilhelm Killing, is a symmetric bilinear form that plays a basic role in the theories of Lie groups and Lie algebras.
(Parse)
(S1 (S (PP (IN In)
(NP (NNS mathematics)))
(, ,)
(NP (NP (DT the) (VBG Killing) (NN form) ('' ') ('' '')) (, ,)
(VP (VBN named)
(PP (IN after)
(NP (NNP Wilhelm) (NN Killing))))
(, ,))
(VP (AUX is)
(NP (NP (DT a) (JJ symmetric) (NN bilinear) (NN form))
(SBAR (WHNP (WDT that))
(S (VP (VBZ plays)
(NP (NP (DT a) (JJ basic) (NN role))
(PP (IN in)
(NP (NP (DT the) (NNS theories))
(PP (IN of)
(NP (NP (NN Lie) (NNS groups)) (CC and)
(NP (NN Lie) (NNS algebras)))
(. .)))