You simply have an incredible talent for teaching. Probably the best on the foreseeable internet as you brilliantly explain both the simplest and quite complex concepts in math. Thank you very much!
In your examples you use an extrinsic embedding space. Can we also use intrinsic properties of the manifold to define the normal vectors and the direct sum with the tangent space to create a "normal space"? Or is the idea that we can leverage the known properties of the embedding space for calculations, so this "normal space" wouldn't be useful?
@@brightsideofmaths than you. I was struggling with coming up with an intrinsic way to define a normal vector. The tangent vectors at least correspond to "directions" that exist on the surface. The normal vector, by definition, does not. Now i can stop thinking about that. 😀
Hi sir I found a printing mistake in your real analysis book that is available on your website. on page no. 17 when you proved third statement i found there is written "Due to b>0" but it is always not possible. there should be |b|>0 that is also mentioned in below. this book is really has a good content for beginners.
![Manifolds 37 | Unit Normal Vector Field [dark version]](http://i.ytimg.com/vi/Zyvyn60MRkc/mqdefault.jpg)
You simply have an incredible talent for teaching. Probably the best on the foreseeable internet as you brilliantly explain both the simplest and quite complex concepts in math. Thank you very much!
Thanks a lot :) If you like it, you can support me on Steady :)
In your examples you use an extrinsic embedding space. Can we also use intrinsic properties of the manifold to define the normal vectors and the direct sum with the tangent space to create a "normal space"?
Or is the idea that we can leverage the known properties of the embedding space for calculations, so this "normal space" wouldn't be useful?
We need some surrounding space to even define normal vectors like here.
@@brightsideofmaths than you. I was struggling with coming up with an intrinsic way to define a normal vector.
The tangent vectors at least correspond to "directions" that exist on the surface.
The normal vector, by definition, does not.
Now i can stop thinking about that. 😀
Hi sir I found a printing mistake in your real analysis book that is available on your website. on page no. 17 when you proved third statement i found there is written "Due to b>0" but it is always not possible. there should be |b|>0 that is also mentioned in below. this book is really has a good content for beginners.
Thanks! I will correct that!