New posts in differential-geometry

How can we show the cone $x^2 +y^2 = z^2$ is not a smooth manifold?

multivariable-calculus differential-geometry partial-derivative

Is there a geometric reason for why every map has a divergence-free Jacobian cofactor matrix?

differential-geometry partial-differential-equations riemannian-geometry calculus-of-variations euler-lagrange-equation

(Quasi)coherent sheaves on smooth manifolds, and their applications

differential-geometry algebraic-geometry sheaf-theory quasicoherent-sheaves

Parallel Transport - Path independence

differential-geometry surfaces

Why is a differential equation a submanifold of a jet bundle?

differential-geometry partial-differential-equations

Constant Curvature Metric and Biholomorphic Equivalence

complex-analysis differential-geometry riemann-surfaces

What is a topology?

general-topology differential-geometry

Calculating the Lie algebra of $SO(2,1)$

differential-geometry lie-groups lie-algebras

Geodesics on the product of manifolds

differential-geometry riemannian-geometry

Covariant derivative versus exterior derivative

differential-geometry differential-forms connections

What the curvature $2$-form really represents?

differential-geometry intuition curvature fiber-bundles principal-bundles

Generalizing results on dynamical systems on $\mathbb{R}^n$ to results on general manifolds

differential-geometry dynamical-systems symplectic-geometry hamilton-equations

Precisely, what is the polar coordinate system?

geometry ordinary-differential-equations multivariable-calculus differential-geometry riemannian-geometry

Quadratic P.S.D. differential operator that is invariant under $\textrm{SL}(2, \mathbb{R})$

functional-analysis differential-geometry lie-groups differential-operators invariance

Covectors $\omega^1, ..., \omega^k$ are linearly dependent iff their wedge product is zero

differential-geometry multilinear-algebra exterior-algebra

notation of differentiation in differential geometry

differential-geometry notation derivatives

Using index notation to write $d^2=0$ in terms of a torsion free connection.

differential-geometry riemannian-geometry

Confused about intuition behind Lie derivative

differential-geometry lie-derivative

Rewriting a integral using a pullback between manifolds with different dimensions

integration differential-geometry smooth-manifolds

Gauss Lemma: metric and coordinates

differential-geometry riemannian-geometry