New posts in differential-geometry

understanding of the first fundamental form

differential-geometry

If $\omega$ is a 2-form on $\mathbb{R}^4$ and $\omega \wedge \omega = 0$, then $\omega$ is decomposable.

differential-geometry differential-forms exterior-algebra

Defining curvature via osculating circles

differential-geometry curves curvature osculating-circle

how to calculate the curvature of an ellipse

differential-geometry manifolds self-learning

Divergence of Gradient of the Unit Normal, and Curvature Equation

calculus differential-geometry multivariable-calculus curvature

Intuition for Cohomology and Holes in a Space

differential-geometry algebraic-topology differential-forms

Reference request: Vector bundles and line bundles etc.

reference-request algebraic-geometry differential-geometry

The differential of the inclusion map is the inclusion map of tangent spaces.

differential-geometry manifolds differential-topology

A difficult question about diffeomorphism about submanifold

differential-geometry differential-topology

What does it mean for Euclidean geometry of the sphere to be inherited from 3-d Space

differential-geometry

"Maximal symmetry" metric for a manifold?

differential-geometry riemannian-geometry

Local diffeomorphism from $\mathbb R^2$ onto $S^2$

differential-geometry

Parametrization of $n$-spheres

general-topology geometry analysis differential-geometry differential-topology

Relations between curvature and area of simple closed plane curves.

geometry differential-geometry plane-curves curvature

How do we obtain a chart for the sphere $\{x:\|x\|=1\}$ from a chart of the ball $\{x:\|x|\le1\}$?

differential-geometry manifolds differential-topology smooth-manifolds manifolds-with-boundary

Hodge Theory, intuition?

differential-geometry algebraic-topology hodge-theory

How to convince a high school student that differentials don't work like fractions in general?

real-analysis multivariable-calculus differential-geometry education

Local existence of parallel vector field

geometry differential-geometry riemannian-geometry

How much algebraic geometry is there in complex geometry (for example, Demailly)?

complex-analysis algebraic-geometry differential-geometry complex-geometry schemes

How can I show that if the second fundamental form of a surface is identically equal to zero, then the surface is a plane?

differential-geometry