Differential Geometry Test

10 Questions | By Droney | Last updated: Mar 22, 2022 | Total Attempts: 1005

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Differential geometry (sweet topic) employs the principles of calculus, both differential and integral as well as multilinear algebra to provide answers to geometry problems. You are challenged to attempt this quiz if you think you understand the tenets of differential geometry. Still, a word of advice—you should ready yourself.

Questions and Answers

1.

These theories are principles on which differential geometry is based except
- A.
  
  Theory of surfaces
- B.
  
  Theory of plane curves
- C.
  
  Theory of space curves
- D.
  
  Theory of dimensional shapes
2.

Differential geometry is intertwined with which of the following?
- A.
  
  Plane geometry
- B.
  
  Differential topology
- C.
  
  Differential equations
- D.
  
  Surface geometry
3.

Which of the following is not a branch of differential geometry?
- A.
  
  Riemannian geometry
- B.
  
  Finsler geometry
- C.
  
  Symplectic geometry
- D.
  
  Plane geometry
4.

Which of the following concepts does not have natural analogues in Remannian geometry?
- A.
  
  Area of plane regions
- B.
  
  Volume of solids
- C.
  
  Arc length of curves
- D.
  
  Circumferences
5.

Which of these is not associated with differential geometry?
- A.
  
  Lorentzian manifold
- B.
  
  Metric tensor
- C.
  
  Finslar manifold
- D.
  
  Differential manifold
6.

Which of the branches of differential geometry is concerned with complex manifolds?
- A.
  
  Complex manifolds
- B.
  
  Symplecfic manifolds
- C.
  
  Riemannian manifolds
- D.
  
  Lorentzian manifold
7.

All of the following are indispensable in differential geometry except
- A.
  
  Vector bundles
- B.
  
  Principal bundles
- C.
  
  Metric tensor
- D.
  
  Connections
8.

The following are applications of differential geometry in physics except
- A.
  
  Electromagnetism
- B.
  
  Thermodynamics
- C.
  
  Gravitational lensing
- D.
  
  Optics
9.

Differential geometry is applied in the following disciplines except
- A.
  
  Computer vision
- B.
  
  Informtion theory
- C.
  
  Structural geology
- D.
  
  Sattelite communication
10.

The mathematical approach upon which differential geometry is based is
- A.
  
  Trigonometry
- B.
  
  Calculus
- C.
  
  Probability
- D.
  
  Logarithms