Best books for self-studying differential geometry
Next semester (fall 2021) I am planning on taking a grad-student level differential topology course but I have never studied differential geometry which is a pre-requisite for the course. My plan is to self-study in the summer and this semester so that I do not have to waste a semester taking a differential geometry course which will ruin my ...
Recommending books for introductory differential geometry
This course is an introduction to differential geometry. The course itself is mathematically rigorous, but still emphasizes concrete aspects of geometry, centered on the notion of curvature. The text used for this course is: Kuhnel, Wolfgang. Differential Geometry: Curves – Surfaces – Manifolds. Student mathematical library, vol. 16.
Extrinsics vs Intrinsics geometry, intuitive explanation
2019年9月5日 · 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 - Introductory texts on manifolds
2022年6月29日 · 3) Manifolds and differential geometry, by Jeffrey Marc Lee (Google Books preview) 4) Also, I just recently recommended this site in answer to another post; the site is from Stanford University; it offers a vast menu of detailed handouts used as the text for a class there on Differential Geometry, each handout accessible/downloadable as a pdf ...
differential geometry - What is a Manifold? - Mathematics Stack …
2015年3月19日 · 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.
differential geometry - divergence of a vector field on a manifold ...
$\begingroup$ This (the formula for the derivative of the metric tensor) seems to be a direct consequence of corrollary 7 in chapter 6 of the second volume of Spivak's comprehensive introduction to differential geometry. $\endgroup$ –
reference request - Where to start learning Differential Geometry ...
2016年10月28日 · You mentioned do Carmo's Differential Geometry of Curves and Surfaces but if you want to study modern differential geometry it may be more appropriate to focus on his excellent text Riemannian geometry, published a decade later. It combines geometric clarity with a teaching experience of decades (do Carmo's, that is).
Research in differential geometry - Mathematics Stack Exchange
2013年10月19日 · See for instance D. Gilbarg, N. Trudinger, "Elliptic Partial Differential Equations of Second Order". Possibly other fields, depending on the differential geometry subarea: Complex analysis, algebraic geometry, geometric topology, measure theory...
In what order should the following areas of mathematics be learned?
Calculus, Discrete Mathematics, and Geometry, are independent enough that their order doesn't matter. Added. However, if by "geometry" you mean analytic geometry, then it should definitely precede calculus, and the same is true if it means trigonometry. I think it unlikely that you meant "differential geometry" or "algebraic geometry", but if ...
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.