##  [Second Fundamental Form](/index.php/second-fundamental-form) 

  ##  [Second Fundamental Form](https://puremath.quantumdictionary.io/second-fundamental-form-0) 

  

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**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The symmetric bilinear form on the tangent space of an immersed submanifold that takes two tangent vectors and returns the normal component of their second derivative in the ambient space; equivalently II_p(u,v)=⟨∇_u v, n⟩ for a chosen unit normal n (with the chosen sign convention).