Differential Geometry of Curves and Surfaces

Carmo, M. P. d. (2016). Differential Geometry of Curves and Surfaces.

Type

Book

Intellectual base

Review or monograph

Year

2016

Pages cited

3-4

ISBN

9780486806990

Link

https://store.doverpublications.com/products/9780486806990

Cited by

3 citations across 3 artifacts.

Domain-specific

• Bonnet Theorem
  • The immersion is unique up to an ambient rigid motion, with orientation and normal conventions handled consistently.
• Intrinsic Equation of a Curve
  • The fundamental theorem of curves supplies that reconstruction-and-uniqueness warrant: sufficiently regular curvature and torsion data determine a unit-speed space curve up to an orientation-preserving Euclidean motion, with the usual positive-curvature qualification for the Frenet frame.
• Second Fundamental Form
  • Do Carmo develops this surface-theory identity and its relation to normal curvature and principal directions.

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