New posts in differential-geometry

Elliptic Bootstrapping for Gauge Transformations

differential-geometry partial-differential-equations gauge-theory

When is an $n$-dimensional manifold characterized by its $m$-dimensional submanifolds?

differential-geometry

What is the universal property of the tangent bundle of a smooth manifold?

differential-geometry

Is the cuspidal cubic $\{y^2 = x^3\} \subset \Bbb R^2$ not smooth?

geometry differential-geometry manifolds smooth-manifolds singularity

Why is the Leibniz rule a sufficient ingredient in the construction of the tangent space?

algebraic-geometry differential-geometry soft-question

Differentiating the determinant of the Jacobian of a diffeomorphism (don't understand a proof)

matrices differential-geometry partial-differential-equations determinant

Lie derivative w.r.t. time-dependent field

differential-geometry differential-forms vector-fields lie-derivative

$f:\mathbb{R}^n \to \mathbb{R}$ has expansion $\sum_i g_i(x)x^i$

multivariable-calculus differential-geometry

A compactly supported continuous function on an open subset of $\mathbb R^n$ is Riemann integrable. What is the relevance of openness in the proof?

real-analysis calculus integration measure-theory differential-geometry

Is $\Bbb R^2\times\Bbb S^2$ homeomorphic to $\Bbb R^4$ with a line removed?

general-topology differential-geometry metric-spaces

How to prove that a vector bundle is trivial iff there are n global sections that form a basis on each fiber?

differential-geometry manifolds vector-bundles

Sectional curvature of product metric?

differential-geometry riemannian-geometry curvature

Homogeneous space and nice manifolds

differential-geometry lie-groups quotient-spaces homogeneous-spaces

Critical Curves of the Energy Functional are Geodesics

differential-geometry manifolds riemannian-geometry calculus-of-variations geodesic

The Ricci flow and $\frac{\partial}{\partial t}g_{ij}=-2(R_{ij}+\nabla_i \nabla_j f)$ are equivalent up to diffeomorphism

differential-geometry riemannian-geometry ricci-flow

Soft question: How does basic differential geometry "fit together"?

differential-geometry soft-question manifolds self-learning

Tangent bundle of sphere as a complex manifold

differential-geometry manifolds differential-topology smooth-manifolds

Explication of the differential of a smooth map

differential-geometry surfaces differential

Is every compact hypersurface contained in a sphere which it touches twice?

differential-geometry

The (orbifold) space of symmetric complex matrix

linear-algebra group-theory differential-geometry algebraic-topology manifolds