53Axx Classical differential geometry
This subtopic introduces the core ideas in classical differential geometry, including foundational concepts, standard methods, and the main questions used to organize the area. Typical uses include building mathematical background, framing related research problems, and supporting applications in neighboring fields where these concepts provide useful structure.
Specific topics
53A04 Curves in Euclidean and related spaces
Overview
Curves in Euclidean and related spaces. This topic covers classical differential geometry of curves and surfaces with emphasis on invariants and geometric constructions.
Related Wikipedia Page
Wikipedia: Differential geometry
Useful Links
Key Ideas
- curves, surfaces, and classical invariants
- moving frames and curvature
- projective and affine differential methods
Typical Uses
Used to analyze local and global behavior of curves and surfaces in classical geometric settings.
Applications
- Computer-aided geometric design
- Geometric mechanics
- Vision and shape analysis
References
Recommended Textbooks
53A05 Surfaces in Euclidean and related spaces
Overview
Surfaces in Euclidean and related spaces. This topic covers classical differential geometry of curves and surfaces with emphasis on invariants and geometric constructions.
Related Wikipedia Page
Wikipedia: Differential geometry
Useful Links
Key Ideas
- curves, surfaces, and classical invariants
- moving frames and curvature
- projective and affine differential methods
Typical Uses
Used to analyze local and global behavior of curves and surfaces in classical geometric settings.
Applications
- Computer-aided geometric design
- Geometric mechanics
- Vision and shape analysis
References
Recommended Textbooks
53A07 Higher-dimensional and -codimensional surfaces in Euclidean $n$-space
Overview
Higher-dimensional and -codimensional surfaces in Euclidean $n$-space. This topic covers classical differential geometry of curves and surfaces with emphasis on invariants and geometric constructions.
Related Wikipedia Page
Wikipedia: Differential geometry
Useful Links
Key Ideas
- curves, surfaces, and classical invariants
- moving frames and curvature
- projective and affine differential methods
Typical Uses
Used to analyze local and global behavior of curves and surfaces in classical geometric settings.
Applications
- Computer-aided geometric design
- Geometric mechanics
- Vision and shape analysis
References
Recommended Textbooks
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
Overview
Minimal surfaces in differential geometry, surfaces with prescribed mean curvature. This topic covers classical differential geometry of curves and surfaces with emphasis on invariants and geometric constructions.
Related Wikipedia Page
Wikipedia: Differential geometry
Useful Links
Key Ideas
- curves, surfaces, and classical invariants
- moving frames and curvature
- projective and affine differential methods
Typical Uses
Used to analyze local and global behavior of curves and surfaces in classical geometric settings.
Applications
- Computer-aided geometric design
- Geometric mechanics
- Vision and shape analysis
References
Recommended Textbooks
53A15 Affine differential geometry
Overview
Affine differential geometry. This topic covers classical differential geometry of curves and surfaces with emphasis on invariants and geometric constructions.
Related Wikipedia Page
Wikipedia: Differential geometry
Useful Links
Key Ideas
- curves, surfaces, and classical invariants
- moving frames and curvature
- projective and affine differential methods
Typical Uses
Used to analyze local and global behavior of curves and surfaces in classical geometric settings.
Applications
- Computer-aided geometric design
- Geometric mechanics
- Vision and shape analysis
References
Recommended Textbooks
53A17 Differential geometric aspects in kinematics
Overview
Differential geometric aspects in kinematics. This topic covers classical differential geometry of curves and surfaces with emphasis on invariants and geometric constructions.
Related Wikipedia Page
Wikipedia: Differential geometry
Useful Links
Key Ideas
- curves, surfaces, and classical invariants
- moving frames and curvature
- projective and affine differential methods
Typical Uses
Used to analyze local and global behavior of curves and surfaces in classical geometric settings.
Applications
- Computer-aided geometric design
- Geometric mechanics
- Vision and shape analysis
References
Recommended Textbooks
53A20 Projective differential geometry
Overview
Projective differential geometry. This topic covers classical differential geometry of curves and surfaces with emphasis on invariants and geometric constructions.
Related Wikipedia Page
Wikipedia: Differential geometry
Useful Links
Key Ideas
- curves, surfaces, and classical invariants
- moving frames and curvature
- projective and affine differential methods
Typical Uses
Used to analyze local and global behavior of curves and surfaces in classical geometric settings.
Applications
- Computer-aided geometric design
- Geometric mechanics
- Vision and shape analysis
References
Recommended Textbooks
53A25 Differential line geometry
Overview
Differential line geometry. This topic covers classical differential geometry of curves and surfaces with emphasis on invariants and geometric constructions.
Related Wikipedia Page
Wikipedia: Differential geometry
Useful Links
Key Ideas
- curves, surfaces, and classical invariants
- moving frames and curvature
- projective and affine differential methods
Typical Uses
Used to analyze local and global behavior of curves and surfaces in classical geometric settings.
Applications
- Computer-aided geometric design
- Geometric mechanics
- Vision and shape analysis
References
Recommended Textbooks
53A30 Conformal differential geometry
Overview
Conformal differential geometry. This topic covers classical differential geometry of curves and surfaces with emphasis on invariants and geometric constructions.
Related Wikipedia Page
Wikipedia: Differential geometry
Useful Links
Key Ideas
- curves, surfaces, and classical invariants
- moving frames and curvature
- projective and affine differential methods
Typical Uses
Used to analyze local and global behavior of curves and surfaces in classical geometric settings.
Applications
- Computer-aided geometric design
- Geometric mechanics
- Vision and shape analysis
References
Recommended Textbooks
53A35 Non-Euclidean differential geometry
Overview
Non-Euclidean differential geometry. This topic covers classical differential geometry of curves and surfaces with emphasis on invariants and geometric constructions.
Related Wikipedia Page
Wikipedia: Differential geometry
Useful Links
Key Ideas
- curves, surfaces, and classical invariants
- moving frames and curvature
- projective and affine differential methods
Typical Uses
Used to analyze local and global behavior of curves and surfaces in classical geometric settings.
Applications
- Computer-aided geometric design
- Geometric mechanics
- Vision and shape analysis
References
Recommended Textbooks
53A40 Other special differential geometries
Overview
Other special differential geometries. This topic covers classical differential geometry of curves and surfaces with emphasis on invariants and geometric constructions.
Related Wikipedia Page
Wikipedia: Differential geometry
Useful Links
Key Ideas
- curves, surfaces, and classical invariants
- moving frames and curvature
- projective and affine differential methods
Typical Uses
Used to analyze local and global behavior of curves and surfaces in classical geometric settings.
Applications
- Computer-aided geometric design
- Geometric mechanics
- Vision and shape analysis
References
Recommended Textbooks
53A45 Differential geometric aspects of vector fields, operators
Overview
Differential geometric aspects of vector fields, operators. This topic covers classical differential geometry of curves and surfaces with emphasis on invariants and geometric constructions.
Related Wikipedia Page
Wikipedia: Differential geometry
Useful Links
Key Ideas
- curves, surfaces, and classical invariants
- moving frames and curvature
- projective and affine differential methods
Typical Uses
Used to analyze local and global behavior of curves and surfaces in classical geometric settings.
Applications
- Computer-aided geometric design
- Geometric mechanics
- Vision and shape analysis
References
Recommended Textbooks
53A55 Differential invariants (local theory), geometric objects
Overview
Differential invariants (local theory), geometric objects. This topic covers classical differential geometry of curves and surfaces with emphasis on invariants and geometric constructions.
Related Wikipedia Page
Wikipedia: Differential geometry
Useful Links
Key Ideas
- curves, surfaces, and classical invariants
- moving frames and curvature
- projective and affine differential methods
Typical Uses
Used to analyze local and global behavior of curves and surfaces in classical geometric settings.
Applications
- Computer-aided geometric design
- Geometric mechanics
- Vision and shape analysis
References
Recommended Textbooks
53A60 Differential geometry of webs
Overview
Differential geometry of webs. This topic covers classical differential geometry of curves and surfaces with emphasis on invariants and geometric constructions.
Related Wikipedia Page
Wikipedia: Differential geometry
Useful Links
Key Ideas
- curves, surfaces, and classical invariants
- moving frames and curvature
- projective and affine differential methods
Typical Uses
Used to analyze local and global behavior of curves and surfaces in classical geometric settings.
Applications
- Computer-aided geometric design
- Geometric mechanics
- Vision and shape analysis
References
Recommended Textbooks
53A70 Discrete differential geometry
Overview
Discrete differential geometry. This topic covers classical differential geometry of curves and surfaces with emphasis on invariants and geometric constructions.
Related Wikipedia Page
Wikipedia: Differential geometry
Useful Links
Key Ideas
- curves, surfaces, and classical invariants
- moving frames and curvature
- projective and affine differential methods
Typical Uses
Used to analyze local and global behavior of curves and surfaces in classical geometric settings.
Applications
- Computer-aided geometric design
- Geometric mechanics
- Vision and shape analysis
References
Recommended Textbooks