1. A

2. B

3. C

4. D

5. E

6. F

7. G

8. H

9. I

10. L

11. M

12. N

13. P

14. S

15. T

16. V

17. W

This is a glossary of terms specific to differential geometry and differential topology. The following three glossaries are closely related:

• Glossary of general topology
• Glossary of algebraic topology
• Glossary of Riemannian and metric geometry.

See also:

• List of differential geometry topics

Words in italics denote a self-reference to this glossary.

A

B

Bundle, see fiber bundle.

C

Codimension. The codimension of a submanifold is the dimension of the ambient space minus the dimension of the submanifold.

Cotangent bundle, the vector bundle of cotangent spaces on a manifold.

D

M and N, a bijective map from M to N is called a diffeomorphism if both and its inverse are smooth functions.

Doubling, given a manifold M with boundary, doubling is taking two copies of M and identifying their boundaries.

As the result we get a manifold without boundary.

E

F

Fiber. In a fiber bundle, π: E → B the preimage π⁻¹(x) of a point x in the base B is called the fiber over x, often denoted E_x.

Frame. A frame at a point of a differentiable manifold M is a basis of the tangent space at the point.

Frame bundle, the principal bundle of frames on a smooth manifold.

G

H

Hypersurface. A hypersurface is a submanifold of codimension one.

I

L

Lens space. A lens space is a quotient of the 3-sphere (or (2n + 1)-sphere) by a free isometric action of Z_k.

M

Manifold. A topological manifold is a locally Euclidean Hausdorff space. (In Wikipedia, a manifold need not be paracompact or second-countable.) A C^k manifold is a differentiable manifold whose chart overlap functions are k times continuously differentiable. A C^∞ or smooth manifold is a differentiable manifold whose chart overlap functions are infinitely continuously differentiable.

N

Neat submanifold. A submanifold whose boundary equals its intersection with the boundary of the manifold into which it is embedded.

P

Parallelizable. A smooth manifold is parallelizable if it admits a smooth global frame. This is equivalent to the tangent bundle being trivial.

Principal bundle. A principal bundle is a fiber bundle P → B together with an action on P by a Lie group G that preserves the fibers of P and acts simply transitively on those fibers.

S

Submanifold, the image of a smooth embedding of a manifold.

Surface, a two-dimensional manifold or submanifold.

Systole, least length of a noncontractible loop.

T

Tangent bundle, the vector bundle of tangent spaces on a differentiable manifold.

Tangent field, a section of the tangent bundle. Also called a vector field.

Transversality. Two submanifolds M and N intersect transversally if at each point of intersection p their tangent spaces and generate the whole tangent space at p of the total manifold.

V

Vector bundle, a fiber bundle whose fibers are vector spaces and whose transition functions are linear maps.

Vector field, a section of a vector bundle. More specifically, a vector field can mean a section of the tangent bundle.

W

Whitney sum. A Whitney sum is an analog of the direct product for vector bundles. Given two vector bundles α and β over the same base B their cartesian product is a vector bundle over B ×B. The diagonal map induces a vector bundle over B called the Whitney sum of these vector bundles and denoted by α⊕β.

• Greek Cyclamen
• Greek cyclamen
• Greek Cypriot nationalism
• Greek deities
• Greek destroyer Adrias
• Greek destroyer Aetos
• Greek destroyer Aetos (1911)
• Greek destroyer Aigaion (L95)
• Greek destroyer Aspis
• Greek destroyer Aspis (1906)
• Greek destroyer Chios
• Greek destroyer Doxa
• Greek destroyer Hydra (D97)
• Greek destroyer Ierax
• Greek destroyer Ierax (1911)
• Greek destroyer Kanaris
• Greek destroyer Kountouriotis
• Greek destroyer Kountouriotis (D99)
• Greek destroyer Kriti
• Greek destroyer Leon
• Greek destroyer Leon (1911)
• Greek destroyer Lonchi
• Greek destroyer Miaoulis
• Greek destroyer Navarinon (1944)
• Greek destroyer Nearchos