---
title: Connections
description: Connections define how geometric objects move along curves on a manifold, generalizing the concept of directional derivatives. Learners will understand parallel transport, covariant differentiation, and how connections relate to curvature in differential geometry.
category: mathematics
subcategory: differential-geometry
difficulty: beginner, intermediate, advanced
url: /subject/connections
---

# Connections

Connections define how geometric objects move along curves on a manifold, generalizing the concept of directional derivatives. Learners will understand parallel transport, covariant differentiation, and how connections relate to curvature in differential geometry.

## Available Resources

1 Courses • 2 Websites

## Websites

### 1. nLab: Connection

Short disambiguation entry listing the meanings of connection in mathematics: connections on bundles (principal, affine, Cartan, Ehresmann, flat), Hurewicz connections, and variants for dg-algebras, corings, cubical sets and double categories, each linking to its own detailed nLab page.

**Difficulty:** Beginner | **Price:** Free

**Link:** https://ncatlab.org/nlab/show/connection

**Tags:** connections, principal-bundles, differential-geometry, ehresmann-connection, nlab

### 2. Wolfram MathWorld

**Author:** Eric W. Weisstein

MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.

**Difficulty:** Intermediate | **Language:** English | **Price:** Free

**Link:** https://mathworld.wolfram.com

**Tags:** mathematics-reference, encyclopedia, abstract-algebra, number-theory, geometry

## Courses

### 1. Geometrical Anatomy of Theoretical Physics

Explore the deep connections between geometry and theoretical physics with Frederic Schuller's insightful course. Learn geometrical anatomy!

**Difficulty:** Advanced | **Price:** Free

**Link:** https://www.youtube.com/playlist?list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic

**Tags:** differential-geometry, manifolds, principal-bundles, connections, lie-groups, mathematical-physics

---

*This content is part of Dantes.io - Your Treasure Map to Knowledge*

*Curated by humans at Dantes.io. Personal study use welcome; republishing this curation requires permission (team@dantes.io).*

View this page online: https://dantes.io/subject/connections