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 A question about differential form
  • · Replies 8 ·
Replies
8
Views
2K
Graduate Two questions for vector bundles
  • · Replies 18 ·
Replies
18
Views
2K
Graduate Vector Rotation About Arbitrary Axis
  • · Replies 8 ·
Replies
8
Views
2K
Graduate The restriction of differential form
  • · Replies 10 ·
Replies
10
Views
2K
Graduate How to Calculate Gauss Curvature from a Mesh Surface?
  • · Replies 2 ·
Replies
2
Views
1K
Graduate Why is a conserved vector field a gradient of a certain func
  • · Replies 3 ·
Replies
3
Views
1K
Graduate Tangent spaces at different points on a manifold
  • · Replies 63 ·
3
Replies
63
Views
10K
Graduate How Do Indices Affect Tensor Notation?
  • · Replies 7 ·
Replies
7
Views
3K
Graduate Calculating Volume of Arbitrary Cross-Section Triangles
  • · Replies 17 ·
Replies
17
Views
4K
Graduate Differential Geometry page 193 Nakahara
  • · Replies 17 ·
Replies
17
Views
2K
Graduate Writing a general curve on a manifold given a metric
  • · Replies 7 ·
Replies
7
Views
2K
Graduate Why phi component is not taken into account for vector R ?See attachment.
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Engineering a body with an intrinsic curvature
  • · Replies 16 ·
Replies
16
Views
2K
Graduate Meaning of Curl from stokes' theorem
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Understanding Index Notation: Simplifying Tensor and Vector Equations
  • · Replies 8 ·
Replies
8
Views
2K
Graduate Transverse Vector: Definition & Meaning
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Are Skew Lines Considered Perpendicular in 3D with Parallel Vectors?
  • · Replies 6 ·
Replies
6
Views
2K
Graduate Interpreting Curl in Vector Fields: ∇×v
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Meaning of isomorphism/diffeomorphism ## f: R^n\to M^m##
  • · Replies 36 ·
2
Replies
36
Views
6K
Graduate Calculating mixed partial derivatives on a 3D mesh
  • · Replies 6 ·
Replies
6
Views
3K
Graduate Geometrical meaning of Curl(Gradient(T))=0
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Coordinate transformation - NED and ECEF frames
  • · Replies 2 ·
Replies
2
Views
12K
Graduate Finding the sine of the angle between 2 rays
  • · Replies 16 ·
Replies
16
Views
2K
Graduate Taylor expansion of the square of the distance function
  • · Replies 9 ·
Replies
9
Views
5K
Graduate Is x^2 + y^2 = 4R^2 a Cylinder or a Circle in 3D Space?
  • · Replies 8 ·
Replies
8
Views
2K
Graduate Is There a Solution to the Inconvenient Expression for Area and Element of Area?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate ##x+y## on a Riemannian manifold
  • · Replies 22 ·
Replies
22
Views
3K
Graduate Geometry on a Sphere: Euclidean or Something Else?
  • · Replies 12 ·
Replies
12
Views
3K
Graduate Calculate the distance travelled in a moving circumference?
  • · Replies 4 ·
Replies
4
Views
1K
Graduate Ricci rotation coefficients and non-coordinate bases
  • · Replies 10 ·
Replies
10
Views
5K
Graduate How Can I Simplify an Equation Involving Levi-Civita Tensors and Indices?
  • · Replies 8 ·
Replies
8
Views
2K
Graduate Manifolds: extrinsic and intrinsic
  • · Replies 5 ·
Replies
5
Views
4K
Graduate Riemannian Metric Tensor & Christoffel Symbols: Learn on R2
  • · Replies 7 ·
Replies
7
Views
2K
Graduate Types of Rotations - Hi Everybody, Ask Your Questions Here
  • · Replies 5 ·
Replies
5
Views
4K
Graduate Lie derivative of tensor field with respect to Lie bracket
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Curved surfaces that do not preserve area
  • · Replies 11 ·
Replies
11
Views
2K
Graduate Angle and trig definitions in curved space
  • · Replies 2 ·
Replies
2
Views
1K
Graduate Difference between Manifolds and Non-Euclidean spaces
  • · Replies 9 ·
Replies
9
Views
7K
Graduate Vector fields transverse to the boundary of a manifold
  • · Replies 6 ·
Replies
6
Views
3K
Graduate Proving K+U is constant with tensor notation.
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Charting Manifolds: Tips & Techniques
  • · Replies 9 ·
Replies
9
Views
3K
Graduate Riemannin generalization of the Taylor expansion
  • · Replies 3 ·
Replies
3
Views
5K
Graduate How to relate the Ehresmann connection to connection 1-form?
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Lie derivative of two left invariant vector fields
  • · Replies 3 ·
Replies
3
Views
5K
Graduate Logic behind definition of Reparametrization
  • · Replies 2 ·
Replies
2
Views
1K
Graduate What are the Discret Subgroups of O(1,3)?
  • · Replies 3 ·
Replies
3
Views
1K
Graduate Understanding fractional and higher dimensions
  • · Replies 13 ·
Replies
13
Views
2K
Graduate Why is ##x = r \sin{\phi} \cos{\theta}## in spherical coordinates?
  • · Replies 26 ·
Replies
26
Views
4K
Graduate Product of a symmetric and antisymmetric tensor
  • · Replies 4 ·
Replies
4
Views
9K
Graduate Curvature implying Closedness in N dimensions
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Finding Coefficients of Orthogonal Quadric Equations
  • · Replies 6 ·
Replies
6
Views
3K
Graduate Calculating the Solid Angle Subtended by a Disc: How to Find ω?
  • · Replies 3 ·
Replies
3
Views
4K
Graduate How Do Tangents Differ Between y²=4ax and x²=4ay?
  • · Replies 6 ·
Replies
6
Views
2K
Graduate Are Global and Local Coordinate Charts Different in Differentiable Manifolds?
  • · Replies 16 ·
Replies
16
Views
2K
Graduate Why Does (\partial_{\mu}\phi)^2 Equal (\partial_{\mu}\phi)(\partial^{\mu}\phi)?
  • · Replies 3 ·
Replies
3
Views
1K
Graduate Is This Contraction of a Tensor Allowed?
  • · Replies 4 ·
Replies
4
Views
1K
Graduate Can someone verify this definition for Weyl tensor?
  • · Replies 7 ·
Replies
7
Views
2K
Graduate Questions about the differential
  • · Replies 32 ·
2
Replies
32
Views
4K
Graduate Tangent vector as derivation question
  • · Replies 9 ·
Replies
9
Views
3K
Graduate Implicit Function Theorem Generalization
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Can contraction of a tensor be defined without using coordinates?
  • · Replies 2 ·
Replies
2
Views
4K
Graduate Learn Submanifold Definition in Differential Geometry
  • · Replies 17 ·
Replies
17
Views
3K
Graduate Get vector position projected on line
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Definition of tensors - abstract and concrete
  • · Replies 5 ·
Replies
5
Views
3K
Graduate How to prove the bilinearity of a given metric using tensorial product addition?
  • · Replies 4 ·
Replies
4
Views
2K
Graduate What is the mistake in my coordinate transformation for Theorema Egregium?
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Projection of a point from one plane onto another
  • · Replies 7 ·
Replies
7
Views
3K
Graduate Local parameterizations and coordinate charts
  • · Replies 14 ·
Replies
14
Views
4K
Graduate Equidistant points on the suface of a sphere
  • · Replies 16 ·
Replies
16
Views
10K
Graduate Raising and Lowering Indices and metric tensors
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Differentiating maps between vector spaces
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Displacement Operator: Exponential of Parameter & Vector?
  • · Replies 8 ·
Replies
8
Views
3K
Graduate Coordinate charts and change of basis
  • · Replies 17 ·
Replies
17
Views
3K
Graduate Understanding the Gradient in Different Coordinate Systems
  • · Replies 14 ·
Replies
14
Views
3K
Graduate Calculating Area on Sphere: Unit Sphere & Rings
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Are There Special Properties of Geodesics in a Lie Group?
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Could someone critique this? (Lie Group with the Lie Algebra)
  • · Replies 14 ·
Replies
14
Views
3K
Graduate Calculus on Manifolds: Lie Algebra, Lie Groups & Exterior Algebra
  • · Replies 7 ·
Replies
7
Views
3K
Graduate What are the key differences between a manifold and a submanifold?
  • · Replies 9 ·
Replies
9
Views
4K
Graduate Torus parametrization and inverse
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Differential map between tangent spaces
  • · Replies 12 ·
Replies
12
Views
4K
Graduate Proof of dimension of the tangent space
  • · Replies 8 ·
Replies
8
Views
2K
Graduate Principal normal and curvature of a helix
  • · Replies 6 ·
Replies
6
Views
3K
Graduate Infinitesimal displacement in spherical coordinates
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Understanding the Tensor Product of Two One-Forms in Differential Geometry
  • · Replies 2 ·
Replies
2
Views
2K
Graduate As accurately as possible draw a curve in the real space R2
  • · Replies 2 ·
Replies
2
Views
1K
Graduate Surface joining two points in a family of concentric spheres
  • · Replies 9 ·
Replies
9
Views
2K
Graduate The speed of a curve in different coordinate systems
  • · Replies 4 ·
Replies
4
Views
1K
Graduate Why is a gradient not always a vector
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Problem with definition of tensor
  • · Replies 10 ·
Replies
10
Views
2K
Graduate Proof the shortest path on a sphere is the great circle.
  • · Replies 10 ·
Replies
10
Views
11K
Graduate Projection stereographic and second fundamental form
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Counting Degrees of Freedom in Tensor
  • · Replies 13 ·
Replies
13
Views
5K
Graduate Ricci tensor equals zero implies flat splace?
  • · Replies 3 ·
Replies
3
Views
4K
Graduate Curve extrapolation: polynomial or Bézier?
  • · Replies 8 ·
Replies
8
Views
4K
Graduate Noethers theorem, physics and mathematics
  • · Replies 7 ·
Replies
7
Views
4K
Graduate How to derive the formula for moment of inertia of polygon?
  • · Replies 2 ·
Replies
2
Views
3K
Graduate A technical question that has to do with Hodge Star
  • · Replies 8 ·
Replies
8
Views
2K
Graduate 'curve-in' condition in an equiangular spiral
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Minimal Surface between two different coaxial circules
  • · Replies 7 ·
Replies
7
Views
2K