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.
Graduate What is the Bing Metrization Theorem?
  • · Replies 2 ·
Replies
2
Views
4K
Graduate Question about the Nagata-Smirnov metrization theorem
  • · Replies 11 ·
Replies
11
Views
4K
Graduate Diffeomorphisms and embedded submanifolds
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Question: vector integral in non-orthog coordinates
  • · Replies 1 ·
Replies
1
Views
2K
Graduate What are some examples of mixed tensors in physics?
  • · Replies 6 ·
Replies
6
Views
2K
Graduate Lebesgue Measurability of Translated Sets?
  • · Replies 2 ·
Replies
2
Views
2K
Graduate About coordinate transformations in general
  • · Replies 43 ·
2
Replies
43
Views
9K
Graduate Is There a Missing Factor in the Nijenhuis Bracket Formula?
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Deriving the Lattice Growth Formula
  • · Replies 6 ·
Replies
6
Views
3K
Graduate A compactification theorem issue
  • · Replies 8 ·
Replies
8
Views
2K
Graduate Question regarding Munkres' proof of the Tychonoff theorem
  • · Replies 13 ·
Replies
13
Views
6K
Graduate Problem from A Beautiful Mind
  • · Replies 8 ·
Replies
8
Views
15K
Graduate Manipulating vector-matrices combinations
  • · Replies 7 ·
Replies
7
Views
3K
Graduate Expressing cos(2π/n) without using trigonometric functions
  • · Replies 7 ·
Replies
7
Views
5K
Graduate 2Questions: 1)Def. of Reg. Neighhoods 2)Zero in Homlgy and Hmtpy.
  • · Replies 3 ·
Replies
3
Views
2K
Graduate A question about the Urysohn metrization theorem
  • · Replies 8 ·
Replies
8
Views
4K
Graduate How can you geometrically see the homotopy between S^n/S^m and S^n-m-1?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Is this formula applicable for defining max{u*,v*} as an outer measure on X?
  • · Replies 5 ·
Replies
5
Views
4K
Graduate Vectyor bundles with all zero characteristic classes
  • · Replies 19 ·
Replies
19
Views
6K
Graduate Calculus of variations on odd dimensional manifolds
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Does \(\tilde{y}^{j}\) depend on \(x^{i}\) in the tangent bundle framework?
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Fast Computation of Fundamental Groups: Practical Methods and Tricks
  • · Replies 7 ·
Replies
7
Views
3K
Graduate No Quadrilateral/Pentagon Knots: Simple Closed Polygons are Trivial
  • · Replies 4 ·
Replies
4
Views
4K
Graduate Is a bundle with non-orientable fibers always trivial?
  • · Replies 7 ·
Replies
7
Views
4K
Graduate Ontoness and Induced Maps on Fundamental Group.
  • · Replies 7 ·
Replies
7
Views
3K
Graduate Isotopy between overlapping and non-over. Dehn Twists.
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Periodic curve as immersed submanifold
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Why does a map from simply connected space to U(1) factors through R?
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Spreading points evenly in plane
  • · Replies 4 ·
Replies
4
Views
4K
Graduate Distance formula in hyperbolic metric
  • · Replies 2 ·
Replies
2
Views
5K
Graduate What is the connection between the mapping class group of a torus and Gl(2,Z)?
  • · Replies 2 ·
Replies
2
Views
4K
Graduate So, the two definitions are equivalent.
  • · Replies 6 ·
Replies
6
Views
4K
Graduate Converting Rotation Matrices (Left handed to Right handed)
  • · Replies 2 ·
Replies
2
Views
11K
Graduate Maps B2->S2 Define F+ & F-: Show Int w S2 = Int F+*(w) B2 - Int F-*(w)
  • · Replies 7 ·
Replies
7
Views
3K
Graduate Geometric Example of Torsion Cycles and Relative Cycles (in Homology)
  • · Replies 17 ·
Replies
17
Views
9K
Graduate What is the rank of the matrix of a reimannienne metric ?
  • · Replies 7 ·
Replies
7
Views
2K
Graduate Definition of a 1-forme différentiel \alpha ^{X}
  • · Replies 2 ·
Replies
2
Views
2K
Graduate What is the topological characterization of the Cantor set?
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Is every orientation form on a compact smooth manifold closed?
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Does a Compact Manifold Imply a Compact Tangent Bundle?
  • · Replies 6 ·
Replies
6
Views
3K
Graduate Gradient in Spherical Coordinates: Computing w/ {em} & {wm}
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Differential Geom: Determining Partial Derivatives of f
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Covariant vs contravariant indices
  • · Replies 7 ·
Replies
7
Views
7K
Graduate How is this possible/ what does it mean?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate How Are Maurer-Cartan Forms Utilized in Physics?
  • · Replies 6 ·
Replies
6
Views
7K
Graduate Non degeneracy of critical points
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Quotient Topology Explained: A Primer for Beginners
  • · Replies 6 ·
Replies
6
Views
10K
Graduate How Do Generalized Poisson Brackets Apply to Canonical Relativity?
  • · Replies 3 ·
Replies
3
Views
9K
Graduate Rotation of plane tangential to sphere
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Introduction to Topology Resources
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Are Same-Action Deck Transformations & Loops Equal for S1 x S1?
  • · Replies 8 ·
Replies
8
Views
6K
Graduate Problem in proving d(x,y)=0 implies x=y.
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Difference between a convex norm and strong convex norme ?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Distances with non-euclidean metric
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Understanding the Automatic Formation of Lie Subgroups in a Lie Group
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Covering Space Action of Z on R2−{0}: Exploring φ
  • · Replies 12 ·
Replies
12
Views
4K
Graduate How to Determine Current Directions from an Electrical Conductivity Tensor?
  • · Replies 4 ·
Replies
4
Views
15K
Graduate How do we compute the geodesic between two points on a flat manifold?
  • · Replies 7 ·
Replies
7
Views
3K
Graduate Covariant derivative and vector functions
  • · Replies 1 ·
Replies
1
Views
2K
Graduate What is a Twistor: Explaining Geometric Applications
  • · Replies 10 ·
Replies
10
Views
3K
Graduate Differing definitions of an inner product
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Tychonoff's theorem and convergent subsequence
  • · Replies 11 ·
Replies
11
Views
4K
Graduate Is Jurdjevic's Definition of Differential Forms an Alternative Approach?
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Interpreting Intersection Form in H_1(K)
  • · Replies 13 ·
Replies
13
Views
3K
Graduate Vector field as smooth embedding
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Hausdorff dimension of the Cantor Set
  • · Replies 1 ·
Replies
1
Views
4K
Graduate Why Do We Minimize the Squared Length in Surface Distance Calculations?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Calculate point on line, perpendicular and intersecting another line in 3d space
  • · Replies 1 ·
Replies
1
Views
5K
Graduate Finding the Metric in Stereographic Projection
  • · Replies 8 ·
Replies
8
Views
5K
Graduate What Is the Geometric Difference in Intersection Forms Q(a,b) vs Q(b,a)?
  • · Replies 0 ·
Replies
0
Views
2K
Graduate Zero curvature => straight line proof
  • · Replies 1 ·
Replies
1
Views
14K
Graduate Nonvanishing section for direct sum of Mobius band
  • · Replies 1 ·
Replies
1
Views
3K
Graduate How to show that a transverse intersection is clean, but not conversely?
  • · Replies 4 ·
Replies
4
Views
4K
Graduate Are Metric Space Infimums Equal for Non-Empty Subsets?
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Example of Codimension-1 Manifolds that are not Isotopic.?
  • · Replies 2 ·
Replies
2
Views
2K
Graduate What is the fundamental group of X?
  • · Replies 11 ·
Replies
11
Views
3K
Graduate The Codimension of a singularity
  • · Replies 4 ·
Replies
4
Views
3K
Graduate About the coherent topology wiki page
  • · Replies 1 ·
Replies
1
Views
4K
Graduate Is the One-Form d \theta Well-Defined at the North and South Pole on a 2-Sphere?
  • · Replies 5 ·
Replies
5
Views
9K
Graduate What does it mean for a change of variables to be UNITARY?
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Exponential Map of R3: A Closer Look
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Can Odd Degree Maps from S^3 to RP^3 Be Constructed Smoothly?
  • · Replies 20 ·
Replies
20
Views
5K
Graduate Is the Closed Unit Square Homeomorphic to the Closed Unit Disc?
  • · Replies 3 ·
Replies
3
Views
5K
Graduate What is the surface parametrization for rotating y=Cosh(x) about the x-axis?
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Integration in Sean Carroll's parallel propagator derivation
  • · Replies 2 ·
Replies
2
Views
4K
Graduate Finsler Geometry: What is the Quadratic Restriction?
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Defining Metrics on Submanifolds: Is G = goi* a Valid Approach?
  • · Replies 2 ·
Replies
2
Views
3K
Graduate What is the meaning of constant on each others fibres in differential geometry?
  • · Replies 9 ·
Replies
9
Views
3K
Graduate If I want to learn about tensor mathematics - where do I need to start
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Point Set Topology: Non-Trivial Facts Beyond Uryshon's Lemma
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Can We Define the Tangent Bundle of a Vector Space V?
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Definition of a sub-elliptic differential operator
  • · Replies 2 ·
Replies
2
Views
2K
Graduate How Accurate Is the Spherical Law of Cosines for Calculating Distances?
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Is every one-dimensional manifold orientable?
  • · Replies 1 ·
Replies
1
Views
5K
Graduate Covariant derivate same as normal derivative?
  • · Replies 3 ·
Replies
3
Views
3K
Graduate How to show 2-tori is diffeomorphic to S^3
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Trouble with Algebraic Geometry in General
  • · Replies 9 ·
Replies
9
Views
4K
Graduate Covariant derivative of the metric
  • · Replies 3 ·
Replies
3
Views
4K
Graduate Proving F is an Isometry for C^1 Functions in Elementary Geometry
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Orientation preserving reparameterization
  • · Replies 2 ·
Replies
2
Views
3K