Differential Geometry Forum

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Join experts in discussing differential geometry topics. This includes manifolds, Tensors and forms. Connections and curvature also. Differential and algebraic topology discussion.
Undergrad Question on tangent space and jet spaces
  • mnb96
  • · Replies 4 ·
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High School Dilating or expanding a closed ball in Riemannian geometry
  • johnconner
  • · Replies 7 ·
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7
Undergrad Differential Geometry: Comparing Metric Tensors
  • dsaun777
  • · Replies 37 ·
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High School Question about Mercator's projection
  • 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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High School What makes pressure a tensor quantity?
  • vtheone
  • · Replies 7 ·
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Undergrad Computing the Directional Derivative ....
  • 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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Undergrad Deriving the area of a spherical triangle from the metric
  • Arman777
  • · Replies 19 ·
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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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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 ·
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Undergrad What is the formula for plotting an accelerating involute curve?
  • homerwho
  • · Replies 5 ·
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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 Connection between 1-Forms and Fourier Transform
  • 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 ·
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Undergrad Defining a Point on a Manifold: Intrinsic vs Embedded Space
  • 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 Question about geodesics 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 Aristotle's Absolute Space & Time: Explained
  • Thytanium
  • · Replies 6 ·
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6
Undergrad Understanding the definition of derivative
  • 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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Graduate Why the terms - exterior, closed, exact?
  • observer1
  • · Replies 6 ·
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Undergrad Question about a partial derivative
  • 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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Graduate Two Covariant Derivatives (Chain Rule)?
  • berlinspeed
  • · Replies 7 ·
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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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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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Graduate Kinematics of surface integrals question
  • skybobster
  • · Replies 1 ·
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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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Undergrad About the definition of a Manifold
  • cianfa72
  • · Replies 20 ·
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Graduate Div and curl operators in a left-handed coordinate system?
  • Aidyan
  • · Replies 1 ·
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Undergrad Larger assignment on Vector Fields
  • MarkBrezina
  • · Replies 3 ·
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3
Graduate Can anyone alive derive these quaternion equations?
  • 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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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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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 Computing Curvature: 2D Plane & Axi-Symmetric 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 Exploring the Power of Geometric Calculus: 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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Graduate Volume using pseudo-spherical coordinates
  • conservative
  • · Replies 1 ·
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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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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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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 Defining the Tensor Product of Gradients for 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 Transversality unlocks the secrets of the manifold?
  • aboutammam
  • · Replies 19 ·
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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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Graduate Fractional spacetime, dimension equation
  • jk22
  • · Replies 1 ·
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1
Undergrad Uncovering the Derivative of a Tensor: Understanding its Equations and Origins
  • mk9898
  • · Replies 6 ·
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6
Undergrad What's the difference between graph, locus & manifold?
  • swampwiz
  • · Replies 24 ·
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24