New posts in differential-geometry

How to look at the Lie derivative as a partial differential operator?

differential-geometry partial-differential-equations differential-topology differential-operators

Inside /outside test of the point on 2D plane

differential-geometry euclidean-geometry analytic-geometry coordinate-systems plane-geometry

Shortest path on hyperboloid

geometry differential-geometry hyperbolic-geometry calculus-of-variations

The Gaussian and Mean Curvatures of a Parallel Surface

differential-geometry surfaces

Bound of $D\exp$ in Riemannian manifold with $|\text{sec} M| \leq K$ and $\text{inj}M \geq i_0$

differential-geometry riemannian-geometry

Best Fit Line with 3d Points

linear-algebra geometry differential-geometry linear-regression

Neighborhood deformation retract for the image of a curve

differential-geometry differential-topology

Tangent space of quotient space

abstract-algebra differential-geometry differential-topology lie-groups lie-algebras

Find a diffeomorphism between $SO(3)$ and $\mathbb{R}P^3$

general-topology differential-geometry manifolds differential-topology

Diffeomorphism $f:U\to V$ then $Df:\mathbb{R^n}\to\mathbb{R^m}$ will be linear isomorphism hence $n=m$

multivariable-calculus differential-geometry differential-topology

A curve where all tangent lines are concurrent must be straight line

differential-geometry

Is every loop in a 3-manifold homotopic to some loop on its boundary?

differential-geometry algebraic-topology differential-topology homotopy-theory

Sanity check: Is every T-principal bundle over T trivial?

differential-geometry algebraic-topology fiber-bundles

Proving rigorously a map preserves orientation

differential-geometry

What does the symbol $\operatorname{Tr}$ in the Yang-Mills action mean?

differential-geometry mathematical-physics quantum-field-theory gauge-theory

Control the sectional curvature

differential-geometry riemannian-geometry

Notation: subscript vs. superscript for coordinate vector fields

linear-algebra differential-geometry notation vector-analysis

Proof behind $S^n\cong SO(n+1)/SO(n)$

linear-algebra abstract-algebra differential-geometry

The Dido problem with an arclength constraint

differential-geometry euclidean-geometry plane-curves

Is $x^3-6xy+y^2=-108$ a regular submanifold but not a regular $k$-submanifold?

general-topology geometry differential-geometry manifolds differential-topology