Learned by Reading
In Wikipedia:
A metric tensor is defined to be a nondegenerate symmetric bilinear form on each tangent space, which varies smoothly from point to point.
(Parse)
(S1 (S (NP (DT A) (JJ metric) (NN tensor))
(VP (AUX is)
(VP (VBN defined)
(S (VP (TO to)
(VP (AUX be)
(NP (NP (DT a) (JJ nondegenerate) (JJ symmetric) (NN bilinear) (NN form))
(PP (IN on)
(NP (DT each) (JJ tangent) (NN space)))
(, ,)
(SBAR (WHNP (WDT which))
(S (VP (VBZ varies) (ADVP (RB smoothly))
(PP (PP (IN from)
(NP (NN point)))
(PP (TO to)
(NP (NN point))))
(. .)))
In Wikipedia:
Explicitly, the metric is a symmetric bilinear form on each tangent space of “M” which varies in a smooth (or differentiable) manner from point to point.
(Parse)
(S1 (S (ADVP (RB Explicitly)) (, ,)
(NP (DT the) (NN metric))
(VP (AUX is)
(NP (NP (DT a) (JJ symmetric) (NN bilinear) (NN form))
(PP (IN on)
(NP (DT each) (JJ tangent) (NN space)))
(PP (IN of) ('' '')
(NP (NNP M) ('' '')
(SBAR (WHNP (WDT which))
(S (VP (VBZ varies)
(PP (IN in)
(NP (DT a) (JJ smooth) (PRN (-LRB- -LRB-) (CC or) (JJ differentiable) (-RRB- -RRB-)) (NN manner)))
(PP (PP (IN from)
(NP (NN point)))
(PP (TO to)
(NP (NN point)))))
(. .)))