Join experts in discussing differential geometry topics. This includes manifolds, Tensors and forms. Connections and curvature also. Differential and algebraic topology discussion.
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Graduate About Chern number of U(1) principal bundle on a torus
- lichen1983312
- · Replies 28 ·
Graduate Stokes' Theorem and Curvature on a Torus
- lichen1983312
- · Replies 7 ·
Undergrad Metric tensor : raising/lowering indices
- tb87
- · Replies 2 ·
Undergrad Levi-Civita properties in 4 dimensions
- Phys pilot
- · Replies 1 ·
Undergrad How does dui = ai·dr = ai·aj·duj in metric tensor derivation?
- kidsasd987
- · Replies 1 ·
Undergrad Proving Stokes' Theorem: General Cases and the Fundamental Theorem of Calculus
- davidge
- · Replies 9 ·
Undergrad Mean and Gaussian curvature for a Gaussian 'hill' seem wrong
- Zaent
- · Replies 6 ·
Undergrad Problem when solving example with differential forms
- davidge
- · Replies 4 ·
Undergrad Integrals: Why Change from M to $\phi(M)$?
- davidge
- · Replies 3 ·
Graduate Extracting Tensor Algebra Term with SU(N) Generators and Numbers
- spaghetti3451
- · Replies 1 ·
Graduate Is there a natural paring between homology and cohomology?
- lichen1983312
- · Replies 19 ·
Undergrad Is Second rank tensor always tensor product of two vectors?
- arpon
- · Replies 2 ·
Graduate Can the Frenet Serret Frame Aid in Arc Length Parameterizations?
- rabbed
- · Replies 19 ·
Graduate Is the Gradient a Covector and the Cross Product a Pseudovector?
- zwierz
- · Replies 20 ·
The tangent and the normal to the conic
- debrajr
- · Replies 1 ·
Find the equation of the conicoid
- debrajr
- · Replies 1 ·
Undergrad Worked example on a covariant vector transformation
- Dyatlov
- · Replies 4 ·
Undergrad Curvature forms and Riemannian curvatures of connections
- RockyMarciano
- · Replies 53 ·
Graduate Why need one-parameter diffeomorphisms to define the Lie derivative
- Frank Castle
- · Replies 9 ·
Undergrad Lie groups left invariant vector fields
- Mikeey aleex
- · Replies 3 ·
Graduate How is the nodal line redefined when body-fixed axes rotate?
- ftft
- · Replies 3 ·
Graduate Pullback and Pushforward in Manifolds: Why Do We Do It?
- observer1
- · Replies 4 ·
Formula for Ellipse 'Change of Distance by Change of Theta'?
- SquishyWeRRa
- · Replies 1 ·
Undergrad Chart coordinate maps of topological manifolds
- Mikeey aleex
- · Replies 1 ·
Undergrad Term for curves at constant distance in 3D space
- nomadreid
- · Replies 8 ·
Undergrad Formula for |∇X|² in coordinates on a Riemannian manifold
- user2010
- · Replies 2 ·
Graduate Conformal flatness of Riemannian manifolds
- RockyMarciano
- · Replies 5 ·
Graduate Tangent Bundle: Why It's Important
- observer1
- · Replies 2 ·
High School What would things look like if PI = 3.
- phillovix
- · Replies 5 ·
Undergrad Ave length of intersection of all lines through a unit cube
- bahamagreen
- · Replies 4 ·
High School About the surface area of a prolate ellipsoid
- Tahmeed
- · Replies 3 ·
Graduate Methods to interpolate surfaces from gradient field?
- grumpymrgruff
- · Replies 1 ·
Undergrad Winding number for a point that lies over a closed curve
- pigna
- · Replies 4 ·
Undergrad Here There be Dragons in Sympletic Geometry
- jedishrfu
- · Replies 2 ·
Graduate Principal bundle triviality, groups and connections
- RockyMarciano
- · Replies 6 ·
Undergrad Determining Coordinate Transformations for Cloaking Device
- Lizard
- · Replies 1 ·
Undergrad Why is the area of a circular cap on a sphere not equal to πr^2?
- JohnnyGui
- · Replies 11 ·
Undergrad Ricci curvatures determine Riemann curvatures in 3-dimension
- tommyxu3
- · Replies 3 ·
Undergrad Difference between 1-form and gradient
- meteo student
- · Replies 14 ·
Undergrad Deriving Frenet-Serret Formulas: Why -τᴿ?
- Arya Prasetya
- · Replies 3 ·
Undergrad Is There a Faster Way to Prove Smoothness on Manifolds?
- JonnyG
- · Replies 2 ·
Undergrad Conservation of dot product with parallel transport
- fab13
- · Replies 9 ·
Graduate Why is cohomology practical if cochain groups are just abstract homomorphisms?
- lichen1983312
- · Replies 7 ·
Graduate Understanding Exact vs. Closed Forms for Mechanical Engineers
- observer1
- · Replies 3 ·
Graduate The meaning of an integral of a one-form
- observer1
- · Replies 9 ·
Graduate Period matrix of the Jacobian variety of a curve
- GogoJS
- · Replies 2 ·
Graduate Why is a short exact sequence split if C is free abelian?
- lichen1983312
- · Replies 21 ·
Graduate What Determines the Degree of the Gauss Map in Differential Geometry?
- spaghetti3451
- · Replies 5 ·
Graduate Two cones connected at their vertices do not form a manifold
- Heisenberg1993
- · Replies 14 ·
Undergrad Why can't we define horizontal spaces as the complement of vertical in a principal bundle?
- hideelo
- · Replies 3 ·
Undergrad How is a manifold locally Euclidean?
- FallenApple
- · Replies 10 ·
Graduate Metric on ℝ^2 Invariant under Matrix Transformations
- FrederikPhysics
- · Replies 1 ·
Graduate Oscillating Plane and Z axis - Energy Balance
- Questionable Thought
- · Replies 1 ·
Undergrad What does this notation mean? (suffix/prefix on tensors?)
- sa1988
- · Replies 2 ·
Graduate Difference between free G-action and effective G-action?
- pellman
- · Replies 1 ·
Undergrad Computing the Weingarten Map L by raising an index
- Leo Mar
- · Replies 2 ·
Graduate How Does the Volume Form on the Unit Sphere Relate to Its Position Vector?
- spaghetti3451
- · Replies 7 ·
High School Calculating a straight line within a sphere
- DaveC426913
- · Replies 7 ·
Graduate Why the Chern numbers (integral of Chern class) are integers?
- lichen1983312
- · Replies 12 ·
High School Curve where both x and y approach infinity
- Pjpic
- · Replies 6 ·
Undergrad Commutator of covariant derivatives
- naima
- · Replies 5 ·
Undergrad Geometric meaning of vector components in curvilinear coordinates
- TonyEsposito
- · Replies 2 ·
Graduate Theory of Surfaces and Theory of Curves Relationship
- ltkach2015
- · Replies 5 ·
Undergrad How do I calculate the surface area of a rotated curve?
- ddddd28
- · Replies 2 ·
Graduate Differential forms and vector calculus
- spaghetti3451
- · Replies 10 ·
Undergrad Meaning of the sign of the geodesic curvature
- Leo Mar
- · Replies 3 ·
Graduate Interior products, exterior derivatives and one forms
- spaghetti3451
- · Replies 3 ·
Undergrad Torsion on cylinder described differentially
- MicroCosmos
- · Replies 2 ·
Undergrad How to write a Vector Field in Cylindrical Co-ordinates?
- greswd
- · Replies 4 ·
Graduate Torsion forms and particle physics
- itssilva
- · Replies 5 ·
Graduate Line integrals of differential forms
- spaghetti3451
- · Replies 1 ·
Graduate Definition of the Lie derivative
- spaghetti3451
- · Replies 2 ·
Undergrad How are Vectors described in Bispherical Coordinates?
- tade
- · Replies 10 ·
Graduate Square of the exterior derivative
- spaghetti3451
- · Replies 10 ·
Undergrad Prove ∇(A x B) = (∇ x A)⋅B - (∇ x B)⋅A where A,B are vectors
- goggles31
- · Replies 5 ·
Graduate What does log G mean in the Ricci form equation?
- lichen1983312
- · Replies 3 ·
Graduate Action of a vector on the pull-back of a function
- spaghetti3451
- · Replies 1 ·
Undergrad Make a Pseudo-Riemannian Metric Conformal
- tommyxu3
- · Replies 3 ·
Undergrad What shape is the ecliptic as seen from Earth?
- Pjpic
- · Replies 1 ·
Graduate Unique separation of the vertical and horizontal spaces?
- lichen1983312
- · Replies 2 ·
Undergrad (Index Notation) Summing a product of 3 numbers
- throneoo
- · Replies 4 ·
High School Trying to represent a written geometrical description
- CollinsArg
- · Replies 1 ·
High School Deriving the Polar of a Point on a Conic
- Appleton
- · Replies 4 ·
Undergrad Levi-Civita symbol index contraction steps
- Waxterzz
- · Replies 3 ·
Undergrad Confusion on Bianchi Identity proof
- Dazed&Confused
- · Replies 2 ·
Undergrad Lie derivative of a differential form
- daxowax
- · Replies 2 ·
Graduate Existence of Complex Structures and Characteristic Classes
- WWGD
- · Replies 4 ·
Graduate Maurer–Cartan forms for a matrix group?
- lichen1983312
- · Replies 2 ·
Undergrad Describing position on an ellipse as a function of angle
- tomwilliam2
- · Replies 2 ·
Graduate Tangent Bundle questions about commutative diagram
- orion
- · Replies 20 ·
Undergrad Notation in Spivak's Calculus on Manifolds
- Z90E532
- · Replies 1 ·
Undergrad Conformal geometry vs. projective geometry
- Lapidus
- · Replies 1 ·
Finding Distinct and Singular Normals for a Parabola
- Theia
- · Replies 2 ·
Undergrad How directrix for other than parabola?
- symbolipoint
- · Replies 1 ·
First Approach to Differential Forms
- Math Amateur
- · Replies 10 ·
Undergrad Intuition on divergence and curl
- cgiustini
- · Replies 3 ·
Undergrad Questions about gradient and scalar product
- space-time
- · Replies 1 ·
High School Base space Minkowski, fiber is S^1, total spaces?
- Spinnor
- · Replies 10 ·
Undergrad Rotation and Translation coordinates
- FrederikPhysics
- · Replies 5 ·
Undergrad Example of computing geodesics with 2D polar coordinates
- fab13
- · Replies 1 ·