- #1

Math Amateur

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## Summary:

- The thread concerns a basis for a tangent space ...

I am reading Andrew McInerney's book: First Steps in Differential Geometry: Riemannian, Contact, Symplectic ... and I am focused on Chapter 3: Advanced Calculus ... and in particular on Section 3.3: Geometric Sets and Subspaces of ##T_p ( \mathbb{R}^n )## ... ...

I need help with an aspect of the proof of Theorem 3.3.14 ... ...

Theorem 3.3.14 reads as follows:

Can someone please explain/demonstrate explicitly why/how ##(e_1)_p, (e_2)_p, \ ... \ ... \ , (e_{n-1} )_p## are the standard basis vectors for ##T_p( S_f )## ...

Help will be much appreciated ... ...

Peter

==================================================================================================================

The above post mentions Theorem 3.3.13 so I am providing text of the theorem together with a relevant definition ... as follows:

Hope that helps readers follow the post ...

Peter

I need help with an aspect of the proof of Theorem 3.3.14 ... ...

Theorem 3.3.14 reads as follows:

Can someone please explain/demonstrate explicitly why/how ##(e_1)_p, (e_2)_p, \ ... \ ... \ , (e_{n-1} )_p## are the standard basis vectors for ##T_p( S_f )## ...

Help will be much appreciated ... ...

Peter

==================================================================================================================

The above post mentions Theorem 3.3.13 so I am providing text of the theorem together with a relevant definition ... as follows:

Hope that helps readers follow the post ...

Peter