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

Undergrad Einstein summation convention confusion

  • dyn
  • · Replies 5 ·
Replies
5

High School Does the equation x² + y² = 1 describe a boundary or a surface?

  • pairofstrings
  • · Replies 10 ·
Replies
10

High School Math Equation for Backward Going Curve?

  • pairofstrings
  • · Replies 17 ·
Replies
17

Graduate Hilbert spaces and kets "over" manifolds

  • andresB
  • · Replies 10 ·
Replies
10

Undergrad Trouble understanding contravariant transformations for vectors

  • whisperzone
  • · Replies 1 ·
Replies
1

Undergrad Vector squared in polar coordinates

  • dyn
  • · Replies 10 ·
Replies
10

Graduate What is the geometric approach to mathematical research?

  • kay bei
  • · Replies 2 ·
Replies
2

Undergrad Math Myth: The sum of all angles in a triangle is 180°

  • Greg Bernhardt
  • · Replies 1 ·
Replies
1

Graduate Mapping circular bevel gear profiles to conical surfaces

  • noname12345
  • · Replies 8 ·
Replies
8

Graduate Differential forms on R^n vs. on manifold

  • Kris-L
  • · Replies 4 ·
Replies
4

Undergrad Understanding Geodesic Parametrization on a Sphere

  • Jufa
  • · Replies 3 ·
Replies
3

Graduate On the relationship between Chern number and zeros of a section

  • Othin
  • · Replies 3 ·
Replies
3

Undergrad Definition of tangent space: why germs?

  • strauser
  • · Replies 6 ·
Replies
6

Undergrad Transition Functions and Lie Groups

  • knowwhatyoudontknow
  • · Replies 2 ·
Replies
2

Undergrad Is There a Distinction Between Riemann Metrics in Physics?

  • Killtech
  • · Replies 16 ·
Replies
16

High School Ways to abstract curves or surfaces

  • trees and plants
  • · Replies 19 ·
Replies
19

Graduate Lagrangian for straight line in XY-plane (dependent on time)

  • lambdajitsu
  • · Replies 3 ·
Replies
3

Graduate Why are sheafs defined using abelian groups?

  • dx
  • · Replies 8 ·
Replies
8

Graduate Something about configuration manifolds in classical mechanics

  • wrobel
  • · Replies 2 ·
Replies
2

Graduate Connection between Reciprocal Space and Cotangent Space

  • Phinrich
  • · Replies 29 ·
Replies
29

Graduate On the different ways of determining curvature on manifolds

  • trees and plants
  • · Replies 1 ·
Replies
1

Graduate Is information geometry worth studying?

  • Frabjous
  • · Replies 13 ·
Replies
13

Undergrad What are the restrictions when swapping between geometries in physics?

  • Killtech
  • · Replies 12 ·
Replies
12

Undergrad Does tensor rank mean (m,n) or just total number of indices?

  • George Keeling
  • · Replies 9 ·
Replies
9

Undergrad Pushforward/Pullback of Vector Field

  • knowwhatyoudontknow
  • · Replies 4 ·
Replies
4

Graduate Transformation of coordinate basis

  • Antarres
  • · Replies 9 ·
Replies
9

High School Examples of manifolds not being groups

  • trees and plants
  • · Replies 7 ·
Replies
7

Graduate Natural parametrization of a curve

  • eva_92
  • · Replies 5 ·
Replies
5

Undergrad Position of a point as a function of angular position

  • Andrea Vironda
  • · Replies 7 ·
Replies
7

Undergrad About divergence, gradient and thermodynamics

  • fluidistic
  • · Replies 4 ·
Replies
4

Graduate What is the Concept of Spectral Geometry?

  • mhill
  • · Replies 1 ·
Replies
1

Undergrad Integration of differential forms

  • JonnyG
  • · Replies 5 ·
Replies
5

Undergrad Parallel transport on flat space

  • steve1763
  • · Replies 11 ·
Replies
11

Undergrad Closest point on a plane to a point near the plane

  • kairama15
  • · Replies 6 ·
Replies
6

Undergrad Testing my knowledge of differential forms

  • JonnyG
  • · Replies 4 ·
Replies
4

Undergrad Can Topological Spaces Have Properties Similar to Manifolds?

  • trees and plants
  • · Replies 1 ·
Replies
1

Undergrad Prove the following statement about n-Manifolds

  • LCSphysicist
  • · Replies 6 ·
Replies
6

Undergrad What is the Minkowski metric tensor's trace?

  • LCSphysicist
  • · Replies 3 ·
Replies
3

Undergrad Finding the change in position and angle after moving the rectangle

  • junseok Lee
  • · Replies 4 ·
Replies
4

Graduate What is a Fibre Bundle? A 5 Minute Introduction

  • Greg Bernhardt
  • · Replies 8 ·
Replies
8

What is discrete geometry and what background is needed?

  • evinda
  • · Replies 4 ·
Replies
4

Undergrad Covariant derivatives, connections, metrics, and Christoffel symbols

  • docnet
  • · Replies 4 ·
Replies
4

Undergrad Derived metrics on surfaces of positive curvature

  • lavinia
  • · Replies 5 ·
Replies
5

Undergrad Difference between diffeomorphism and homeomorphism

  • Silviu
  • · Replies 69 ·
3
Replies
69

Undergrad Fixing orientation by fixing a frame in a tangent space

  • Unconscious
  • · Replies 1 ·
Replies
1

Undergrad Riemannian Fisher-Rao metric and orthogonal parameter space

  • Vini
  • · Replies 1 ·
Replies
1

Undergrad How is this a representation of a 3 dimensional torus?

  • docnet
  • · Replies 4 ·
Replies
4

High School Can coordinates be functions in geometry?

  • trees and plants
  • · Replies 6 ·
Replies
6

High School Can Curvature and Geodesics be Generalized in Higher Dimensions?

  • trees and plants
  • · Replies 10 ·
Replies
10

Undergrad What is an (almost) complex manifold in simple words

  • gerald V
  • · Replies 4 ·
Replies
4

Undergrad Are vector components contravariant or covariant, not the vector itself?

  • Hiero
  • · Replies 22 ·
Replies
22

High School Why does the Wikipedia article use a negative sign in the 4-gradient?

  • etotheipi
  • · Replies 7 ·
Replies
7

How do I find the Euclidean Coordinate Functions of a parametrized curve?

  • banananaz
  • · Replies 1 ·
Replies
1

Undergrad Infinitesimal Movement Along 3-d Geodesics

  • kairama15
  • · Replies 1 ·
Replies
1

Undergrad Elliptic Function Rotation Problem

  • Sabertooth
  • · Replies 1 ·
Replies
1

Undergrad Geometry and algebraic equations

  • member 428835
  • · Replies 4 ·
Replies
4

Graduate Parallel transport on a symplectic space

  • andresB
  • · Replies 1 ·
Replies
1

High School Understanding 3D Temperature Direction Change with 8 Corner Points

  • sqljunkey
  • · Replies 6 ·
Replies
6

Graduate Is there an invariant form of the geodesic equation?

  • jk22
  • · Replies 11 ·
Replies
11

High School Increasing the dimensions of a manifold

  • sqljunkey
  • · Replies 1 ·
Replies
1

Undergrad Why Torsion = 0 => Planar Curve in this Proof

  • Rippling Hysteresis
  • · Replies 8 ·
Replies
8

Undergrad Fixing an orientation for a connected smooth surface

  • Unconscious
  • · Replies 4 ·
Replies
4

High School Relating basis vectors at different points in a neighborhood

  • Shirish
  • · Replies 5 ·
Replies
5

High School Standard version of covariant derivative properties

  • Shirish
  • · Replies 5 ·
Replies
5

High School Why can't we define tensor field derivatives by differentiating components?

  • Shirish
  • · Replies 7 ·
Replies
7

Undergrad Are product spaces disjoint unions of fibers in trivial bundles?

  • cianfa72
  • · Replies 15 ·
Replies
15

Undergrad The second fundamental form and derived metrics

  • lavinia
  • · Replies 13 ·
Replies
13

Graduate Can we always rewrite a Tensor as a differential form?

  • kay bei
  • · Replies 8 ·
Replies
8

Graduate How Can I Differentiate Curves Where the Real Part of \( Y(t) \) Vanishes?

  • qbar
  • · Replies 3 ·
Replies
3

High School Why is There No Factor of 1/2 in the Torsion Tensor Definition?

  • Shirish
  • · Replies 3 ·
Replies
3

High School Solving for integral curves- how to account for changing charts?

  • Shirish
  • · Replies 4 ·
Replies
4

High School Reconciling basis vector operators with partial derivative operators

  • Shirish
  • · Replies 4 ·
Replies
4

Undergrad Tangent space basis vectors under a coordinate change

  • Shirish
  • · Replies 12 ·
Replies
12

High School Derivative of a constant scalar field at a point

  • Phinrich
  • · Replies 2 ·
Replies
2

Undergrad Partial Surface Area of a Tube

  • deweyirl
  • · Replies 4 ·
Replies
4

Undergrad Area of an inclined surface with respect to the original surface

  • tent
  • · Replies 5 ·
Replies
5

Undergrad Sachs and Wu's General Relativity for Mathematicians

  • Avogadro Number
  • · Replies 5 ·
Replies
5

Undergrad Directional Derivatives of a vector ----gradient of f(P)----

  • Ishika_96_sparkles
  • · Replies 4 ·
Replies
4

Graduate What Is a Kahler Manifold?

  • s00mb
  • · Replies 7 ·
Replies
7

High School A covariant vs contravariant vector?

  • etotheipi
  • · Replies 5 ·
Replies
5

Undergrad About Covariant Derivative as a tensor

  • cianfa72
  • · Replies 6 ·
Replies
6

Undergrad Why does the isotropic curvature constraint imply maximal symmetry?

  • Wledig
  • · Replies 9 ·
Replies
9

Undergrad Differentiating the Dot Product's Evil Twin

  • Trying2Learn
  • · Replies 2 ·
Replies
2

High School Is my intuitive way of thinking about non-Euclidean geometry valid?

  • SamRoss
  • · Replies 19 ·
Replies
19

Graduate How to understand when surface terms go to zero

  • Ebarval
  • · Replies 6 ·
Replies
6

Undergrad Visualizing the cotangent space to a sphere

  • giulio_hep
  • · Replies 26 ·
Replies
26

Undergrad How Do Transition Functions Define a Möbius Strip in Fiber Bundles?

  • cianfa72
  • · Replies 10 ·
Replies
10

Graduate Are there references and do the converse theorems hold for theorems 1,2?

  • wrobel
  • · Replies 0 ·
Replies
0

Graduate Diffeomorphic manifolds of equal constant curvature

  • C0nstantine
  • · Replies 42 ·
2
Replies
42

Where Do These Parametric Equations and Plane Intersect?

  • aa1604962
  • · Replies 1 ·
Replies
1

Graduate Tangent vector derivation: differentiating pullback vs original field

  • Decimal
  • · Replies 9 ·
Replies
9

Graduate Time derivative of basis frames and the product rule

  • Trying2Learn
  • · Replies 1 ·
Replies
1

Graduate Geodesics of the 2-sphere in terms of the arc length

  • Adrian555
  • · Replies 4 ·
Replies
4

Undergrad Sufficient condition for a vector field to be conservative

  • DottZakapa
  • · Replies 3 ·
Replies
3

Undergrad Living inside a Hopf fibration, seeing the fibers

  • Spinnor
  • · Replies 26 ·
Replies
26

Undergrad Beltrami flows have zero parallel gradients?

  • TheCanadian
  • · Replies 1 ·
Replies
1

Undergrad Geodesics on a sphere and the Christoffel symbols

  • acegikmoqsuwy
  • · Replies 6 ·
Replies
6

High School An intrinsic equation of a surface

  • geordief
  • · Replies 5 ·
Replies
5

Undergrad A set of numbers as a smooth curved changing manifold.

  • Spinnor
  • · Replies 3 ·
Replies
3

Graduate Pullback of the metric from R3 to S2

  • nigelscott
  • · Replies 1 ·
Replies
1