Question

1 :- Let ${\bf E_1}$ , ${\bf E_2 }$ and ${\bf E_3}$ be a frame field on ${\bf E^3 }$ . For each tangent Vector ${\bf V}$ to ${\bf E^3}$ at point ${\bf P}$ . If ${\bf W_{ij} ( V ) = \nabla_{V} E_{i} E_{j} ( P )}$ for ${\bf i , j = 1 , 2 , 3}$ then prove that ${\bf W_{ij}}$ is a 1 - form & ${\bf W_{ij} = - W_{ji}}$ .

2 :- Define Frenet Formula for curvature function of $\beta$

Topic :- Differential Geometry ​

Answer 1

Answer:

refer To attachment plz

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