▁Second - order ▁tensor ▁field ▁ ▁The ▁diver gence ▁of ▁a ▁second - order ▁tensor ▁field ▁is ▁defined ▁using ▁ ▁where ▁a ▁is ▁an ▁arbitrary ▁constant ▁vector . ▁ ▁In ▁cur vil ine ar ▁coordinates , ▁ ▁Lap la cian ▁ ▁S cal ar ▁field ▁The ▁Lap la cian ▁of ▁a ▁scalar ▁field ▁ φ ( x ) ▁is ▁defined ▁as ▁ ▁Using ▁the ▁alternative ▁expression ▁for ▁the ▁diver gence ▁of ▁a ▁vector ▁field ▁gives ▁us ▁ ▁Now ▁ ▁Therefore , ▁ ▁C url ▁of ▁a ▁vector ▁field ▁The ▁curl ▁of ▁a ▁vector ▁field ▁v ▁in ▁cov ari ant ▁cur vil ine ar ▁coordinates ▁can ▁be ▁written ▁as ▁ ▁where ▁ ▁Orth ogonal ▁cur vil ine ar ▁coordinates ▁Assume , ▁for ▁the ▁purposes ▁of ▁this ▁section , ▁that ▁the ▁cur vil ine ar ▁coordinate ▁system ▁is ▁orthogonal , ▁i . e ., ▁▁ ▁or ▁equival ently , ▁▁ ▁where ▁. ▁As ▁before , ▁ ▁are ▁cov ari ant ▁basis ▁vectors ▁and ▁bi , ▁b j ▁are ▁cont rav ari ant ▁basis ▁vectors . ▁ ▁Also , ▁let ▁( e 1 , ▁e 2 , ▁e 3 ) ▁be ▁a ▁background , ▁fixed , ▁Cart esian ▁basis . ▁ ▁A ▁list ▁of ▁orthogonal ▁cur vil ine ar ▁coordinates ▁is ▁given ▁below . ▁ ▁Met ric ▁tensor ▁in ▁orthogonal ▁cur vil ine ar ▁coordinates ▁ ▁Let ▁r ( x ) ▁be ▁the ▁position ▁vector ▁of ▁the ▁point ▁x ▁with ▁respect ▁to ▁the ▁origin ▁of ▁the ▁coordinate ▁system . ▁ ▁The ▁notation ▁can ▁be ▁simplified ▁by