- #1
Vasileios
- 6
- 0
First of all hello,
I am new to this forum and I decided to join in order to exchange some information with other members that are more knowledgeable than me in the area of diff. geometry.
My background is computer science but I am not a student. I am only now starting to learn about diff. geometry (and in particular information geometry which is my interest). So I my questions are going to be mostly basic. Also maybe sometimes my use of terminology is not 100% and i apologise for that, but it will become better in time :)
So the first question I would like to ask is the connection between the first fundamental form and the sq. arc length element [tex]ds^2[/tex]
It seems to me that the first (and second) fundamental forms are only defined for 2d manifolds in [tex]R^3[/tex] whereas the [tex]ds^2[/tex] as the sum of [tex]g_{ij}[/tex] is arbitrarily dimensional. So my question is, is there an equivalent definition for the fundamental forms for higher dimensions or not?
Thanks
Vasileios
I am new to this forum and I decided to join in order to exchange some information with other members that are more knowledgeable than me in the area of diff. geometry.
My background is computer science but I am not a student. I am only now starting to learn about diff. geometry (and in particular information geometry which is my interest). So I my questions are going to be mostly basic. Also maybe sometimes my use of terminology is not 100% and i apologise for that, but it will become better in time :)
So the first question I would like to ask is the connection between the first fundamental form and the sq. arc length element [tex]ds^2[/tex]
It seems to me that the first (and second) fundamental forms are only defined for 2d manifolds in [tex]R^3[/tex] whereas the [tex]ds^2[/tex] as the sum of [tex]g_{ij}[/tex] is arbitrarily dimensional. So my question is, is there an equivalent definition for the fundamental forms for higher dimensions or not?
Thanks
Vasileios
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