Encyclopedia > Differential geometry

  Article Content

Differential geometry

Differential geometry is basically the study of geometry using calculus.

It has many applications in physics, especially in the theory of relativity. The central objects of study are Riemannian manifolds (see also Riemannian geometry): geometrical objects such as surfaces which locally look like Euclidean space and therefore allow the definition of analytical concepts such as tangent vectors and tangent space, differentiability, and vector and tensor fields.

The manifolds are equipped with a metric, which introduces geometry because it allows to measure distances and angles locally and define concepts such as geodesics, curvature and torsion.

All Wikipedia text is available under the terms of the GNU Free Documentation License

  Search Encyclopedia

Search over one million articles, find something about almost anything!
  Featured Article
TLAs from MAA to PZZ

... possible TLAs from YAA to ZZZ MAA MAB[?] MAC MAD MAE[?] MAF[?] MAG[?] MAH[?] MAI[?] MAJ[?] MAK[?] MAL[?] MAM[?] MAN MAO MAP[?] MAQ[?] MAR[?] MAS[?] MAT[?] MAU[?] MAV[?] ...