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.
High School Equation of Circle: Boundary or Surface?
  • pairofstrings
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High School Math Equation for Backward Going Curve?
  • pairofstrings
  • · Replies 17 ·
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Graduate Hilbert spaces and kets "over" manifolds
  • andresB
  • · Replies 10 ·
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Undergrad Trouble understanding contravariant transformations for vectors
  • whisperzone
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Undergrad Vector squared in polar coordinates
  • dyn
  • · Replies 10 ·
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Graduate What is the geometric approach to mathematical research?
  • kay bei
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Undergrad Math Myth: The sum of all angles in a triangle is 180°
  • Greg Bernhardt
  • · Replies 1 ·
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Graduate Help requested with translating math into code (Not homework)
  • noname12345
  • · Replies 8 ·
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Graduate Differential forms on R^n vs. on manifold
  • Kris-L
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Undergrad Understanding Geodesic Parametrization on a Sphere
  • Jufa
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Graduate On the relationship between Chern number and zeros of a section
  • Othin
  • · Replies 3 ·
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Undergrad Definition of tangent space: why germs?
  • strauser
  • · Replies 6 ·
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6
Undergrad Transition Functions and Lie Groups
  • knowwhatyoudontknow
  • · Replies 2 ·
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Undergrad Is There a Distinction Between Riemann Metrics in Physics?
  • Killtech
  • · Replies 16 ·
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16
High School Ways to abstract curves or surfaces
  • trees and plants
  • · Replies 19 ·
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Graduate Lagrangian for straight line in XY-plane (dependent on time)
  • lambdajitsu
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Graduate Why are sheafs defined using abelian groups?
  • dx
  • · Replies 8 ·
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Graduate Something about configuration manifolds in classical mechanics
  • wrobel
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Graduate Connection between Reciprocal Space and Cotangent Space
  • Phinrich
  • · Replies 29 ·
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Graduate On the different ways of determining curvature on manifolds
  • trees and plants
  • · Replies 1 ·
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Graduate Information Geometry: Is there any there there?
  • Frabjous
  • · Replies 13 ·
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13
Undergrad What are the restrictions when swapping between geometries in physics?
  • Killtech
  • · Replies 12 ·
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12
Undergrad Tensor rank: One number or two?
  • George Keeling
  • · Replies 9 ·
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9
Undergrad Pushforward/Pullback of Vector Field
  • knowwhatyoudontknow
  • · Replies 4 ·
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Graduate Transformation of coordinate basis
  • Antarres
  • · Replies 9 ·
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High School Examples of manifolds not being groups
  • trees and plants
  • · Replies 7 ·
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7
Graduate Natural parametrization of a curve
  • eva_92
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5
Undergrad Position of a point as a function of angular position
  • Andrea Vironda
  • · Replies 7 ·
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Undergrad About divergence, gradient and thermodynamics
  • fluidistic
  • · Replies 4 ·
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4
Graduate What is the Concept of Spectral Geometry?
  • mhill
  • · Replies 1 ·
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Undergrad Integration of differential forms
  • JonnyG
  • · Replies 5 ·
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5
Undergrad Parallel transport on flat space
  • steve1763
  • · Replies 11 ·
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Undergrad Closest point on a plane to a point near the plane
  • kairama15
  • · Replies 6 ·
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6
Undergrad Testing my knowledge of differential forms
  • JonnyG
  • · Replies 4 ·
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4
Undergrad Can Topological Spaces Have Properties Similar to Manifolds?
  • trees and plants
  • · Replies 1 ·
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Undergrad Prove the following statement about n-Manifolds
  • LCSphysicist
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Undergrad What is the Minkowski metric tensor's trace?
  • LCSphysicist
  • · Replies 3 ·
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Undergrad Finding the change in position and angle after moving the rectangle
  • junseok Lee
  • · Replies 4 ·
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Graduate What is a Fibre Bundle? A 5 Minute Introduction
  • Greg Bernhardt
  • · Replies 8 ·
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8
Discrete Geometry: Info, Knowledge & More
  • evinda
  • · Replies 4 ·
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4
Undergrad Covariant derivatives, connections, metrics, and Christoffel symbols
  • docnet
  • · Replies 4 ·
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4
Undergrad Derived metrics on surfaces of positive curvature
  • lavinia
  • · Replies 5 ·
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5
Undergrad Difference between diffeomorphism and homeomorphism
  • Silviu
  • · Replies 69 ·
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Undergrad Fixing orientation by fixing a frame in a tangent space
  • Unconscious
  • · Replies 1 ·
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Undergrad Riemannian Fisher-Rao metric and orthogonal parameter space
  • Vini
  • · Replies 1 ·
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1
Undergrad How is this a representation of a 3 dimensional torus?
  • docnet
  • · Replies 4 ·
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4
High School Can coordinates be functions in geometry?
  • trees and plants
  • · Replies 6 ·
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6
High School Can Curvature and Geodesics be Generalized in Higher Dimensions?
  • trees and plants
  • · Replies 10 ·
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Undergrad What is an (almost) complex manifold in simple words
  • gerald V
  • · Replies 4 ·
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4
Undergrad Is a vector itself contra/covariant or just its components?
  • Hiero
  • · Replies 22 ·
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High School Why does the Wikipedia article use a negative sign in the 4-gradient?
  • etotheipi
  • · Replies 7 ·
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How do I find the Euclidean Coordinate Functions of a parametrized curve?
  • banananaz
  • · Replies 1 ·
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Undergrad Infinitesimal Movement Along 3-d Geodesics
  • kairama15
  • · Replies 1 ·
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Undergrad Elliptic Function Rotation Problem
  • Sabertooth
  • · Replies 1 ·
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Undergrad Geometry and algebraic equations
  • member 428835
  • · Replies 4 ·
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4
Graduate Parallel transport on a symplectic space
  • andresB
  • · Replies 1 ·
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High School Understanding 3D Temperature Direction Change with 8 Corner Points
  • sqljunkey
  • · Replies 6 ·
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6
Graduate Exists ? : Invariant geodesic equation
  • jk22
  • · Replies 11 ·
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High School Increasing the dimensions of a manifold
  • sqljunkey
  • · Replies 1 ·
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1
Undergrad Why Torsion = 0 => Planar Curve in this Proof
  • Rippling Hysteresis
  • · Replies 8 ·
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8
Undergrad Fixing an orientation for a connected smooth surface
  • Unconscious
  • · Replies 4 ·
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4
High School Relating basis vectors at different points in a neighborhood
  • Shirish
  • · Replies 5 ·
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5
High School Standard version of covariant derivative properties
  • Shirish
  • · Replies 5 ·
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5
High School Defining the derivative of a vector field component
  • Shirish
  • · Replies 7 ·
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7
Undergrad Product Space vs Fiber Bundle: Understanding the Difference
  • cianfa72
  • · Replies 15 ·
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Undergrad The second fundamental form and derived metrics
  • lavinia
  • · Replies 13 ·
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Graduate Can we always rewrite a Tensor as a differential form?
  • kay bei
  • · Replies 8 ·
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Graduate How Can I Differentiate Curves Where the Real Part of \( Y(t) \) Vanishes?
  • qbar
  • · Replies 3 ·
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High School Why is There No Factor of 1/2 in the Torsion Tensor Definition?
  • Shirish
  • · Replies 3 ·
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High School Solving for integral curves- how to account for changing charts?
  • Shirish
  • · Replies 4 ·
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High School Reconciling basis vector operators with partial derivative operators
  • Shirish
  • · Replies 4 ·
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4
Undergrad Tangent space basis vectors under a coordinate change
  • Shirish
  • · Replies 12 ·
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12
High School Derivative of a constant scalar field at a point
  • Phinrich
  • · Replies 2 ·
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Undergrad Partial Surface Area of a Tube
  • deweyirl
  • · Replies 4 ·
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Undergrad Area of an inclined surface with respect to the original surface
  • tent
  • · Replies 5 ·
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5
Undergrad Sachs and Wu's General Relativity for Mathematicians
  • Avogadro Number
  • · Replies 5 ·
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Undergrad Directional Derivatives of a vector ----gradient of f(P)----
  • Ishika_96_sparkles
  • · Replies 4 ·
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Graduate What Is a Kahler Manifold?
  • s00mb
  • · Replies 7 ·
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High School A covariant vs contravariant vector?
  • etotheipi
  • · Replies 5 ·
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Undergrad About Covariant Derivative as a tensor
  • cianfa72
  • · Replies 6 ·
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Undergrad Understanding the Definition of Isotropic Spaces in Riemannian Manifolds
  • Wledig
  • · Replies 9 ·
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9
Undergrad Differentiating the Dot Product's Evil Twin
  • Trying2Learn
  • · Replies 2 ·
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High School Is my intuitive way of thinking about non-Euclidean geometry valid?
  • SamRoss
  • · Replies 19 ·
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Graduate How to understand when surface terms go to zero
  • Ebarval
  • · Replies 6 ·
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6
Undergrad Visualizing the cotangent space to a sphere
  • giulio_hep
  • · Replies 26 ·
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26
Undergrad How Do Transition Functions Define a Möbius Strip in Fiber Bundles?
  • cianfa72
  • · Replies 10 ·
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Graduate Are there references and do the converse theorems hold for theorems 1,2?
  • wrobel
  • · Replies 0 ·
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Graduate Diffeomorphic manifolds of equal constant curvature
  • C0nstantine
  • · Replies 42 ·
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Where Do These Parametric Equations and Plane Intersect?
  • aa1604962
  • · Replies 1 ·
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Graduate Question about the derivation of the tangent vector on a manifold
  • Decimal
  • · Replies 9 ·
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9
Graduate Simple question on the derivative of base frame
  • Trying2Learn
  • · Replies 1 ·
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Graduate Geodesics of the 2-sphere in terms of the arc length
  • Adrian555
  • · Replies 4 ·
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4
Undergrad Sufficient condition for a vector field to be conservative
  • DottZakapa
  • · Replies 3 ·
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Undergrad Living inside a Hopf fibration, seeing the fibers
  • Spinnor
  • · Replies 26 ·
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26
Undergrad Beltrami flows have zero parallel gradients?
  • TheCanadian
  • · Replies 1 ·
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1
Undergrad Geodesics on a sphere and the Christoffel symbols
  • acegikmoqsuwy
  • · Replies 6 ·
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High School An intrinsic equation of a surface
  • geordief
  • · Replies 5 ·
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Undergrad A set of numbers as a smooth curved changing manifold.
  • Spinnor
  • · Replies 3 ·
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Graduate Pullback of the metric from R3 to S2
  • nigelscott
  • · Replies 1 ·
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Graduate Differential movement along a curved surface
  • kairama15
  • · Replies 3 ·
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3