Differential Geometry Forum

Join experts in discussing differential geometry topics. This includes manifolds, Tensors and forms. Connections and curvature also. Differential and algebraic topology discussion.

Threads

Graduate Differential movement along a curved surface

  • kairama15
  • · Replies 3 ·
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3

Undergrad Question on tangent space and jet spaces

  • mnb96
  • · Replies 4 ·
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4

High School Dilating or expanding a closed ball in Riemannian geometry

  • johnconner
  • · Replies 7 ·
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7

Undergrad Can different metric tensors from different manifolds appear in one equation?

  • dsaun777
  • · Replies 37 ·
2
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37

High School Is Mercator's projection conformal with equal scaling coefficients?

  • jk22
  • · Replies 1 ·
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1

High School What Does the Scalar R Represent in Tensor Mapping on a Smooth Manifold?

  • sqljunkey
  • · Replies 22 ·
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22

High School Why is pressure a tensor quantity?

  • vtheone
  • · Replies 7 ·
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7

Undergrad Directional derivative of f(x)=x in Fortney 2.4(a)(i)

  • Math Amateur
  • · Replies 2 ·
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2

What is the Surface Area of a Square with Given Points and Side Lengths?

  • ghostfirefox
  • · Replies 1 ·
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1

Undergrad Deriving the area of a spherical triangle from the metric

  • Arman777
  • · Replies 19 ·
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19

Graduate Covariant derivative and connection of a covector field

  • Vyrkk
  • · Replies 8 ·
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8

Undergrad How Do Lie Derivatives Connect to Symmetry and Conservation Laws in Physics?

  • pcr
  • · Replies 2 ·
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2

Undergrad Geodesics subject to a restriction

  • MrTictac
  • · Replies 2 ·
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2

Undergrad The vanishing of the covariant derivative of the metric tensor

  • snoopies622
  • · Replies 37 ·
2
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37

Undergrad What is the formula for plotting an accelerating involute curve?

  • homerwho
  • · Replies 5 ·
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5

Undergrad Equivalent paths to the Christoffel symbols

  • snoopies622
  • · Replies 9 ·
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9

High School In higher dimensions, are there more than just rotations and displacements?

  • Hiero
  • · Replies 13 ·
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13

Undergrad Curve Inside a Sphere: Differentiating Alpha

  • Celso
  • · Replies 1 ·
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1

Undergrad Christoffel symbols and covariant derivative intuition

  • physlosopher
  • · Replies 15 ·
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15

Graduate 1-forms as level sets of Fourier phase in 3-D

  • Phinrich
  • · Replies 3 ·
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3

High School How to know if a Euclidean space is not a 3-sphere?

  • jk22
  • · Replies 35 ·
2
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35

Undergrad How to define a point on an embedded manifold intrinsically or using coordinates

  • dsaun777
  • · Replies 6 ·
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6

Undergrad Is a Full-Cone in E^3 a Topological Manifold?

  • cianfa72
  • · Replies 7 ·
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7

Undergrad Invariant properties of metric tensor

  • olgerm
  • · Replies 12 ·
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12

Undergrad "Adding" a Vector Space and its Dual

  • Phinrich
  • · Replies 16 ·
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16

Graduate Is the Berry connection a Levi-Civita connection?

  • Joker93
  • · Replies 5 ·
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5

Undergrad Geodesic equation for great circles on a sphere

  • George Keeling
  • · Replies 4 ·
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4

Undergrad Circumference of a circle on a spherical surface

  • physlosopher
  • · Replies 7 ·
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7

Undergrad Using the derivative of a tangent vector to define a geodesic

  • physlosopher
  • · Replies 7 ·
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7

Undergrad Why can't Galilean spacetime be represented as ordered pairs?

  • Thytanium
  • · Replies 6 ·
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6

Undergrad Why component-wise differentiation of vector fields lacks coordinate independence

  • lriuui0x0
  • · Replies 1 ·
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1

Undergrad What is the Purpose of Calculating the Christoffel Symbols in Curved Spacetime?

  • dsaun777
  • · Replies 11 ·
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11

Undergrad Vector valued integrals in the theory of differential forms

  • Hiero
  • · Replies 4 ·
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4

Undergrad Can the area be understood as the "number of points"?

  • jordi
  • · Replies 27 ·
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27

Graduate Why the terms - exterior, closed, exact?

  • observer1
  • · Replies 6 ·
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6

Undergrad Partial derivative of sin²φ with respect to θ on a sphere

  • George Keeling
  • · Replies 7 ·
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7

Graduate I need some fun questions with answers in differential geometry ()

  • Brian_Dehority
  • · Replies 3 ·
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3

Undergrad Trying to construct a particular manifold locally using a metric

  • dsaun777
  • · Replies 9 ·
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9

Undergrad Derivative of the Ad map on a Lie group

  • eipiplusone
  • · Replies 3 ·
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3

Undergrad Understanding vector differential

  • lriuui0x0
  • · Replies 11 ·
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11

Graduate Two Covariant Derivatives (Chain Rule)?

  • berlinspeed
  • · Replies 7 ·
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7

Undergrad Geodesics under coordinate transformation

  • VladZH
  • · Replies 23 ·
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23

Graduate Book to understand Euler angles (and Tait–Bryan )

  • Avatrin
  • · Replies 1 ·
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1

Graduate Correct differentiation identity? (tensors, vectors)

  • Waldheri
  • · Replies 1 ·
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1

Graduate Rotating Surfaces: Simplifying Sketching with Normalized Equations

  • SprucerMoose
  • · Replies 1 ·
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1

Graduate Kinematics of surface integrals question

  • skybobster
  • · Replies 1 ·
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1

Graduate Looking for a coordinate system

  • coolnessitself
  • · Replies 1 ·
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1

Graduate Uniform distribution on a toroidal surface

  • Barnak
  • · Replies 1 ·
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1

Graduate Partial and Covariant derivatives in invarint actions

  • AlphaNumeric
  • · Replies 1 ·
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1

Undergrad About the definition of a Manifold

  • cianfa72
  • · Replies 20 ·
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20

Graduate Div and curl operators in a left-handed coordinate system?

  • Aidyan
  • · Replies 1 ·
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1

Undergrad Tensor notation for vector products and differential operators

  • MarkBrezina
  • · Replies 3 ·
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3

Graduate Deriving quaternion equations from Hamilton's Lectures section 563

  • Ben2
  • · Replies 3 ·
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3

Undergrad Difference (if any) between E^1 x E^3 and E^4

  • cianfa72
  • · Replies 14 ·
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14

Graduate Is the Exponential Map Always Surjective from Lie Algebras to Lie Groups?

  • giulio_hep
  • · Replies 8 ·
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8

Undergrad Transforming Vector Fields between Cylindrical Coordinates

  • Luke Tan
  • · Replies 1 ·
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1

Graduate Normal derivative in spheroidal coordinate

  • dexturelab
  • · Replies 1 ·
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1

Graduate Geodesics on R^2: Exact Formula?

  • Statis
  • · Replies 1 ·
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1

Undergrad Diffeomorphism invariance and contracted Bianchi identity

  • "Don't panic!"
  • · Replies 7 ·
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7

Graduate Can Manifold Angle Determine Concavity and Convexity of a Curve?

  • sniper
  • · Replies 1 ·
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1

Graduate Cylindrical polar co-ordinates

  • Nylex
  • · Replies 1 ·
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1

Graduate Linear Programming Constraints

  • Kreizhn
  • · Replies 1 ·
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1

Graduate What is geometric group theory and how does it relate to different geometries?

  • diegzumillo
  • · Replies 12 ·
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12

Undergrad Why are scalars and dual vectors 0- and 1-forms?

  • George Keeling
  • · Replies 4 ·
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4

Undergrad Bases for Tangent Spaces and Subspaces - McInerney Theorem 3.3.14

  • Math Amateur
  • · Replies 4 ·
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4

Graduate Geometric Understanding of Octopole Moment Beyond Quadropole

  • shdrums9
  • · Replies 1 ·
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1

Graduate How to predict the shape of the circle from any point of view?

  • OFF_Smog
  • · Replies 1 ·
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1

Graduate Deriving curvature formulas for plane curves and axisymmetric surfaces

  • rsq_a
  • · Replies 1 ·
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1

Graduate 4 dimensional curl as antisymmetric matrix

  • purplegreen
  • · Replies 1 ·
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1

Undergrad Algorithm to determine the roulette curve

  • LAP3141
  • · Replies 1 ·
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1

Graduate How can I find the normals of a Dodecahedron in rational numbers?

  • TheDestroyer
  • · Replies 1 ·
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1

Undergrad Bezier curves, tangent angles, and arc length

  • ZippyDee
  • · Replies 2 ·
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2

Graduate How can we simplify calculating geodesic distances on a deformed Earth?

  • dextercioby
  • · Replies 1 ·
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1

Graduate Minimal Surfaces, Differential Geometry, and Partial Differential Equations

  • octohydra
  • · Replies 1 ·
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1

Undergrad 3d rotation of accelerometer vectors

  • IMK
  • · Replies 1 ·
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1

Graduate Finding the Equation of a Rotated Cone

  • eddo
  • · Replies 1 ·
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1

Graduate Geometric Calculus and differential forms in physics

  • laserblue
  • · Replies 1 ·
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1

Graduate Preparing for STEP: Solving a Sphere Tangency Problem

  • Positronized
  • · Replies 1 ·
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1

Graduate Volume using pseudo-spherical coordinates

  • conservative
  • · Replies 1 ·
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1

Undergrad Mapping Euler spiral (clothoid) parameters

  • rivimey
  • · Replies 1 ·
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1

Graduate Geometry of perspective: apparent projected distance

  • Galap
  • · Replies 1 ·
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1

Graduate Scale factors and the Jacobian Matrix

  • Andromon
  • · Replies 1 ·
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1

Graduate What is the Intuition Behind Unicursal Curves and Their Double Points?

  • bolbteppa
  • · Replies 1 ·
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1

Graduate Why Does the Radius in Parabolic Coordinates Involve √(εη)?

  • bolbteppa
  • · Replies 1 ·
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1

Graduate Non-Convex Coordinate Transform Problem Rotating Frame

  • phil0stine
  • · Replies 2 ·
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2

Undergrad Parameterized surfaces from coordinates

  • Pencilvester
  • · Replies 2 ·
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2

Undergrad How is rotation related to the curl of a vector field?

  • Apashanka
  • · Replies 2 ·
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2

Graduate What Is a Lune on a Sphere and Its Key Properties?

  • Greg Bernhardt
  • · Replies 1 ·
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1

Graduate Definition of Lie Group and its Algebras

  • Greg Bernhardt
  • · Replies 1 ·
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1

Graduate What is the definition of ∇ ⊗ ∇f in different coordinate systems?

  • member 428835
  • · Replies 5 ·
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5

Undergrad Definition of Displacement: Change in Position

  • Greg Bernhardt
  • · Replies 1 ·
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1

Graduate What is a covariant derivative

  • Greg Bernhardt
  • · Replies 1 ·
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1

Graduate What are the key differences between 1-forms and 2-forms in vector spaces?

  • Greg Bernhardt
  • · Replies 1 ·
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1

Graduate What is the Generalized Stokes' Theorem and its Applications?

  • Greg Bernhardt
  • · Replies 1 ·
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1

Graduate What is a Tensor: FAQ Definition/Summary

  • Greg Bernhardt
  • · Replies 1 ·
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1

Graduate Why is transversality important in differential geometry?

  • aboutammam
  • · Replies 19 ·
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19

Graduate Mixed intrinsic and extrinsic angles in 3D rotations

  • aydos
  • · Replies 1 ·
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1

Undergrad Proving that an action is transitive in the orbits

  • Andres316
  • · Replies 8 ·
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8

Graduate Fractional spacetime, dimension equation

  • jk22
  • · Replies 1 ·
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1

Undergrad How does the covariant derivative of a tensor relate to partial derivatives?

  • mk9898
  • · Replies 6 ·
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6