Differential Geometry Forum

Post thread
Join experts in discussing differential geometry topics. This includes manifolds, Tensors and forms. Connections and curvature also. Differential and algebraic topology discussion.
Undergrad An obtuse triangle and its circumcenter
  • · Replies 2 ·
Replies
2
Views
5K
Graduate How Do Basis and Topology Definitions Interact in Set Theory?
  • · Replies 7 ·
Replies
7
Views
5K
Graduate Differential Geometry: Show Regular Curve is Invertible
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Finding new major axis of ellipse after stretching along arbitrary axis
  • · Replies 4 ·
Replies
4
Views
10K
Graduate How Can I Define a Topology on N with Exactly k Limit Points?
  • · Replies 2 ·
Replies
2
Views
3K
Graduate The universal property characterizing the quotient topology
  • · Replies 19 ·
Replies
19
Views
22K
Graduate Comma notation in tensor expression?
  • · Replies 4 ·
Replies
4
Views
14K
Undergrad What Kind of Triangle is ABC in a Square with an Isosceles Triangle?
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad A small rectangle on a large ball - distortion?
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Need Help Understanding Cycloid Rolling vs Slipping
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Analogy between vectors and covectors
  • · Replies 9 ·
Replies
9
Views
5K
Undergrad Plotting the naval territory of a country
  • · Replies 4 ·
Replies
4
Views
3K
High School Do Four Points Define a Hyperplane or Extend Beyond?
  • · Replies 1 ·
Replies
1
Views
7K
Graduate Formal definitions of cutting and pasting etc
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Visualising calabi yau manifolds
  • · Replies 2 ·
Replies
2
Views
4K
Graduate Is the Finite Cartesian Product of Simply Connected Sets Also Simply Connected?
  • · Replies 1 ·
Replies
1
Views
3K
High School Can you have a curved line without a plane?
  • · Replies 14 ·
Replies
14
Views
4K
Graduate Understanding Functional Determinants in Mathematics
  • · Replies 5 ·
Replies
5
Views
6K
Graduate What is the equation for a möbius strip with a constant bend?
  • · Replies 6 ·
Replies
6
Views
4K
Graduate How Do You Calculate the Trace of an Arbitrary Tensor?
  • · Replies 5 ·
Replies
5
Views
4K
Graduate Degree of a Map: Directly Proving k is Degree of f
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Integrating a 2-form on a 2-cube
  • · Replies 2 ·
Replies
2
Views
4K
Graduate Conformal Equivalence: Help with Penrose's Road to Reality
  • · Replies 9 ·
Replies
9
Views
4K
Graduate What is the Definition of 'Cos' in Hyperbolic Geometry?
  • · Replies 8 ·
Replies
8
Views
3K
Graduate How Do Covariant and Contravariant Vectors Differ in Tensor Calculus?
  • · Replies 26 ·
Replies
26
Views
15K
Graduate Conservative vector field; classification of derivative
  • · Replies 1 ·
Replies
1
Views
4K
Undergrad Gradient in spherical coordinates problem
  • · Replies 3 ·
Replies
3
Views
26K
Graduate Ellipse: geometric equivalence of two definitions
  • · Replies 10 ·
Replies
10
Views
7K
Graduate Orientability and Diffeomorphisms of Manifolds
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Can Sard's Theorem Confirm Submanifolds as Measure Zero?
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Visualizing left action of SO(3) on itself
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad How to Calculate surface width of a 3d object intersected at an angle?
  • · Replies 8 ·
Replies
8
Views
5K
Graduate Total Derivative in Curvilinear Coordinates
  • · Replies 6 ·
Replies
6
Views
6K
Undergrad Tensor operations and properties
  • · Replies 3 ·
Replies
3
Views
11K
Graduate Transforming Index to Matrix Form for Amateurs
  • · Replies 11 ·
Replies
11
Views
6K
Graduate Cylindrical section is an ellipse?
  • · Replies 4 ·
Replies
4
Views
4K
Graduate Covariant vectors vs reciprocal vectors
  • · Replies 1 ·
Replies
1
Views
11K
Graduate Produce Scalar from Tensor: What's the Name?
  • · Replies 9 ·
Replies
9
Views
4K
Graduate Indices in differential geometry
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Hyperbolic Circle <=> Euclidean Circle.
  • · Replies 1 ·
Replies
1
Views
6K
Graduate Hyperbolic Distance and double Cross Ratio.
  • · Replies 1 ·
Replies
1
Views
4K
Graduate Finding the Point That Divides an Interval in Hyperbolic Geometry
  • · Replies 20 ·
Replies
20
Views
5K
Graduate The Exterior Covariant Derivative: Understanding Connections and Fibre Bundles
  • · Replies 3 ·
Replies
3
Views
5K
Graduate Vanishing measure of a set with codimenon 2
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Show that there is no immersion of S^n into R^n
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Is the Inverse Jacobian used to Transform Flat Space into Curved Space?
  • · Replies 1 ·
Replies
1
Views
6K
Graduate Dimension of a topological space
  • · Replies 14 ·
Replies
14
Views
7K
Graduate Form of line element of a torus.
  • · Replies 8 ·
Replies
8
Views
7K
Graduate Simple connectivity and finite coverings
  • · Replies 4 ·
Replies
4
Views
4K
Undergrad How Do You Determine the Axis of a Helix?
  • · Replies 15 ·
Replies
15
Views
11K
Undergrad How to Calculate a Circle's Equation in 3D Space?
  • · Replies 3 ·
Replies
3
Views
23K
Graduate Can the homotopy extension property fail on certain pairs of spaces?
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Guide to CW Complexes and n-Cells
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Understanding the Smash Product of Two Topological Spaces
  • · Replies 1 ·
Replies
1
Views
6K
Graduate Divergence of mixed II-order tensors
  • · Replies 1 ·
Replies
1
Views
4K
Graduate Negative Curvature: Can We Draw an Infinite Triangle?
  • · Replies 14 ·
Replies
14
Views
10K
Graduate Gaining Intuitive Understanding of Parallel Transporting Tensors
  • · Replies 14 ·
Replies
14
Views
5K
Graduate About the implicit function theorem
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Can Geodesic Surfaces Minimize Area Like Curves Minimize Length?
  • · Replies 2 ·
Replies
2
Views
4K
Graduate What are the main considerations when defining a smooth manifold?
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Revolving around a sphere helically?
  • · Replies 4 ·
Replies
4
Views
2K
Graduate RP^2 vs CP: Comparing Stenographic Representations
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad 3D Points on Surface of a Pipe (Disk)
  • · Replies 11 ·
Replies
11
Views
4K
Graduate How Can I Create a Diagrammatic Notation Editor for Penrose's Notation?
  • · Replies 5 ·
Replies
5
Views
5K
Graduate Understanding Normal One-Forms for Plane x=0
  • · Replies 1 ·
Replies
1
Views
5K
Undergrad How do you do vector addition in cylindrical coordinates?
  • · Replies 2 ·
Replies
2
Views
8K
Graduate How to Parametrize a 3D Circle and Find the Closest Point?
  • · Replies 5 ·
Replies
5
Views
12K
Graduate Can the Noether current be derived from the electrodynamic Lagrangian?
  • · Replies 4 ·
Replies
4
Views
5K
Graduate Parallelizability vs. hairy ball theorem
  • · Replies 27 ·
Replies
27
Views
11K
Graduate Gaussian Curvature of (x^2+y^2+1)^-2
  • · Replies 1 ·
Replies
1
Views
4K
Graduate Extending a transformation from a curve to the whole space
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Spherical Harmonic Integration
  • · Replies 1 ·
Replies
1
Views
4K
Graduate To transform from flat to curved space
  • · Replies 6 ·
Replies
6
Views
5K
Graduate Can a subset of R^n have multiple centres of symmetry?
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Intuition for Covariant derivative of a Tensor Field
  • · Replies 9 ·
Replies
9
Views
8K
Graduate Coordinates adapted to two vector fields
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Hilbert Manifolds: An Infinite Dimensional Analogy to Smooth Manifolds?
  • · Replies 4 ·
Replies
4
Views
4K
Graduate What Are the Kissing Numbers for Different Sized Spheres in 3D?
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Understanding Tensor Operations: From Multilinear Mappings to Vector Spaces
  • · Replies 9 ·
Replies
9
Views
4K
Graduate Is m a finitely generated ideal over C^{\infty}(M)?
  • · Replies 8 ·
Replies
8
Views
4K
High School What is a Fractal? A 10th Grade Explanation
  • · Replies 1 ·
Replies
1
Views
3K
Graduate How Does a Function on Manifolds Change When Transferred from M to N?
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Where is the Centroid of a Moebius Strip? [SOLVED]
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Topology Question:Connected Components
  • · Replies 1 ·
Replies
1
Views
4K
Graduate Showing SO(3) Subset is Projective Plane Diffeomorphic
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Are vector bundles principal bundles?
  • · Replies 14 ·
Replies
14
Views
9K
Graduate Does Every Coordinate System Admit Local Othornormal Basis Vectors
  • · Replies 5 ·
Replies
5
Views
4K
Graduate Foliation, fibration, fiber bundle?
  • · Replies 1 ·
Replies
1
Views
8K
Graduate How to find rotation parameter in sphere?
  • · Replies 2 ·
Replies
2
Views
6K
Graduate Topology Question: Continuous Functions and Simply Connected Subsets
  • · Replies 6 ·
Replies
6
Views
4K
Graduate Manifolds / Lie Groups - confusing notation
  • · Replies 22 ·
Replies
22
Views
6K
Graduate Proof of Quotient Map Q: A -> R for Exam Review
  • · Replies 3 ·
Replies
3
Views
5K
Graduate Prove Homeomorphism of {A in GL(n;R) | det(A)>0 & det(A)<0}
  • · Replies 4 ·
Replies
4
Views
4K
Graduate Are Diffeomorphic Manifolds Sharing a Unique Property?
  • · Replies 22 ·
Replies
22
Views
8K
Graduate What is the solution to the geodesic equation for a torus?
  • · Replies 14 ·
Replies
14
Views
9K
Graduate Understanding the Power Map in Tensor Analysis: Bishop and Goldberg Page 6
  • · Replies 3 ·
Replies
3
Views
3K
Graduate The Wildest point on an ellipse
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Diagrammatic Notation for Tensors: Worthwhile Learning?
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Understand differentiable manifolds
  • · Replies 3 ·
Replies
3
Views
4K
Graduate What determines the number of differentiable structures on a manifold?
  • · Replies 15 ·
Replies
15
Views
5K