Differential geometry is the application of differential calculus in the setting of smooth manifolds (curves, surfaces and higher dimensional examples). Modern differential geometry focuses on …

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 i...

Another alternative may be Boothby - " Introduction to Differentiable Manifolds and Riemannian Geometry " since it also builds everything up starting from multivariable analysis. If you prefer …

"Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces suitable for a first course on the subject. Prerequisites are kept to an absolute …

Actually this question has been previously asked and well-answered. See Intuitive interpretation of the Laplacian. Also Nice way of thinking about the Laplace operator. Also Why is the Laplacian …

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 …

Mar 20, 2015 · Since you have tagged this as differential geometry, I'll assume you're talking about smooth manifolds. The essential idea is that, if you are an itty-bitty person living in the …

May 8, 2020 · This procedure is called a differential, i.e. a differential is a map on tangent spaces. Then the authors say that to describe a tangent space at x x you should take a chart and apply …

Aug 11, 2020 · 1 I found the most understandable explanation in page-98 of Tristan Needham's Visual Differential Geometry book: If a bead of unit mass is launched at unit speed along a …

Sep 20, 2013 · Where can I find some simple examples of pullbacks and pushforwards between manifolds. Specifically examples that show the details of the computations.