Extrinsics vs Intrinsics geometry, intuitive explanation
Sep 5, 2019 · The simplest results are those in the differential geometry of curves and differential geometry of surfaces. Starting with the work of Riemann, the intrinsic point of view was developed, in which one cannot speak of moving "outside" the geometric object because it is considered to be given in a free-standing way.
differential geometry - Prerequisites for tensor analysis
Jun 28, 2023 · $\begingroup$ Differential geometry is, in my view, one of the absolute pinnacles of modern mathematics. If you want to relearn mathematics "from point zero", as you say, you have a long way to go before you get to this subject, as you correctly said in your post.
reference request - Roadmap for learning differential geometry ...
Aug 29, 2024 · The first semester graduate level differential geometry course where I was an undergraduate (actually, this course was primarily intended as a course providing machinery and background in manifolds for more advanced work in differential geometry, which was typically done in graduate student seminars), usually taken by 2nd or 3rd year graduate ...
differential geometry - Manifolds and Charts - Mathematics Stack …
This is why differential geometry in Euclidean space is so much easier-the space comes equipped with very natural charts(i.e. Cartesian,plane and cylindrical polar coordinates,spherical coordinates). You're in luck since differential geometry of all the mathematical disciplines, has the largest number of clear textbooks for self learning.
differential geometry - Deriving calculation formulas for torsion …
Mar 25, 2015 · $\begingroup$ The numerator of $\tau$ is a scalar triple product.There are a number of identities about them. Other possibly useful facts include $\Vert v \Vert^2 = v \cdot v$ and $\Vert v \times w \Vert^2 = \Vert v \Vert^2 \Vert w \Vert^2 - (v \cdot w
Concrete examples and computations in differential geometry
Sep 29, 2015 · I've been studying differential geometry by myself for some time now. I studied a fair amount of the basic general theory and gone through a lot of the exercises from several textbooks. Lately I started to realize how huge (and daunting) differential geometry really is. I think I have a pretty solid grasp of the basic objects.
differential geometry - What is a Manifold? - Mathematics Stack …
Mar 19, 2015 · Also, there is the mathematical practicality that you want every point of the manifold to be inside and not on the edge of some set, particularly if you're doing calculus or differential geometry. You want a one-size-fits all, seamless, definition: you don't want to have to be dealing with onesided limits at edges of a partition.
Intuition about pullbacks in differential geometry
The book thath helped me clear the confusion about differential forms is A geometric approach to differential forms by Bachman and it has many excerscises and examples. When you feel comfortable you can move to Tu's Introduction to Manifolds.
Software for differential geometry - Mathematics Stack Exchange
Aug 29, 2012 · I'm interested in computations with vector-valued differential forms on Riemannien manifolds. Wedge product, exterior derivative, likely Hodge dual, tensor product, contractions of all kinds. Basically just rewriting and then possibly casting equations into a given base.
differential geometry - What is a differetial structure, exactly ...
Jan 31, 2019 · The point with the fact that every atlas determines a unique differential structure is it allow us to define and talk about a differential structure without worry about the maximal one. We are not able to exhibit a maximal atlas, it is just a theorical concept, but we are able to exhibit an atlas, for example a finite one, in concrete examples ...