Chandrasekhar–Wentzel lemma
In vector calculus, Chandrasekhar–Wentzel lemma was derived by Subrahmanyan Chandrasekhar and Gregor Wentzel in 1965, while studying the stability of rotating liquid drop. The lemma states that "if formula_1 is a surface bounded by a simple closed contour formula_2, then Here formula_4 is the position vector and formula_5 is the unit normal on the surface. An immediate consequence is that if formula_1 is a closed surface, then the line integral tends to zero, leading to the result, or, in index notation, we have That is to say the tensor defined on a closed surface is always  symmetric, i.e., formula_10. Proof. Let us write the vector in index notation, but summation convention will be avoided throughout the proof. Then the left hand side can be written as Converting the line integral to surface integral using Stokes's theorem, we get Carrying out the requisite differentiation and after some rearrangement, we get or, in other words, And since formula_15, we have thus proving the lemma.