New posts in differential-geometry

Exterior algebra of a vector bundle

differential-geometry exterior-algebra

Milnor fundamental theorem of algebra : proof that $f: S^2 \rightarrow S^2$ is smooth

complex-analysis differential-geometry differential-topology smooth-manifolds smooth-functions

Question regarding baby do Carmo's definition of a regular surface.

multivariable-calculus derivatives differential-geometry definition

Closed space curves of constant curvature

differential-geometry

Is the chart function of a smooth manifold a differomorphism, not just a homeomorphism

differential-geometry

Why first fundamental form?

differential-geometry

Triviality of a tautological bundle

differential-geometry

Using Stokes' theorem to define the exterior derivative operator

differential-geometry

Extension of Riemannian Metric to Higher Forms

differential-geometry riemannian-geometry multilinear-algebra

understanding covariant derivative (connexion)

differential-geometry riemannian-geometry

How can a $C^1$-continuous surface have infinite curvature?

differential-geometry continuity curvature

Why define $(\nabla^2F)(X,Y)=\nabla_X(\nabla_YF)-(\nabla_{\nabla_XY}F)$?

differential-geometry riemannian-geometry

A very small disc winds around a larger circular disc of radius $R$ connected to it by a string. How long is the spiral it travels?

calculus geometry algebra-precalculus differential-geometry

Intuition on Kulkarni-Nomizu product

differential-geometry riemannian-geometry tensor-products

Deriving Finsler geodesic equations from the energy functional

multivariable-calculus differential-geometry euler-lagrange-equation finsler-geometry

Showing a vector field is tangent to the 2-sphere

differential-geometry

The Sphere Does Not Admit a Metric Isometry into a Euclidean Space.

differential-geometry riemannian-geometry

Explicit Hodge decomposition on $T^2$

differential-geometry hodge-theory

Geodesic of a curved surface

differential-geometry riemannian-geometry surfaces

Definition of $dz_i\otimes d\bar{z_j}(\frac{\partial}{\partial z_m},c\frac{\partial}{\partial z_n})$

differential-geometry differential-forms complex-geometry