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 Levi-Civita properties in 4 dimensions
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Undergrad Understanding the Derivation of the Metric Tensor
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Undergrad Proving Stokes' Theorem: General Cases and the Fundamental Theorem of Calculus
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Undergrad Mean and Gaussian curvature for a Gaussian 'hill' seem wrong
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Undergrad Problem when solving example with differential forms
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Undergrad Integrals: Why Change from M to $\phi(M)$?
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Graduate Extracting Tensor Algebra Term with SU(N) Generators and Numbers
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Graduate Is there a natural paring between homology and cohomology?
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Undergrad Is Second rank tensor always tensor product of two vectors?
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Graduate Can the Frenet Serret Frame Aid in Arc Length Parameterizations?
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Graduate Is the Gradient a Covector and the Cross Product a Pseudovector?
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MHB The tangent and the normal to the conic
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MHB Find the equation of the conicoid
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Undergrad Worked example on a covariant vector transformation
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Undergrad Curvature forms and Riemannian curvatures of connections
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Graduate Diffeomorphisms & the Lie derivative
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Undergrad Lie groups left invariant vector fields
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Graduate About the nodal line in defining Euler angles
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Graduate Pullback and Pushforward in Manifolds: Why Do We Do It?
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MHB Formula for Ellipse 'Change of Distance by Change of Theta'?
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Undergrad Chart coordinate maps of topological manifolds
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Undergrad Term: generalization of parallel curves to 3D
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Undergrad Norm of Laplacian Let: Formula for | ∇X|² in Coordinates
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Graduate Conformal flatness of Riemannian manifolds
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Graduate Tangent Bundle: Why It's Important
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High School What would things look like if PI = 3.
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Undergrad Ave length of intersection of all lines through a unit cube
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High School About the surface area of a prolate ellipsoid
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Graduate Methods to interpolate surfaces from gradient field?
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Undergrad Winding number for a point that lies over a closed curve
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Undergrad Here There be Dragons in Sympletic Geometry
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Graduate Principal bundle triviality, groups and connections
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Undergrad Determining Coordinate Transformations for Cloaking Device
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Undergrad Why is the area of a circular cap on a sphere not equal to πr^2?
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Undergrad Ricci curvatures determine Riemann curvatures in 3-dimension
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Undergrad Difference between 1-form and gradient
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Undergrad Deriving Frenet-Serret Formulas: Why -τᴿ?
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Undergrad Is There a Faster Way to Prove Smoothness on Manifolds?
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Undergrad Conservation of dot product with parallel transport
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Graduate Very basic question about cohomology.
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Graduate Understanding Exact vs. Closed Forms for Mechanical Engineers
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Graduate The meaning of an integral of a one-form
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Graduate Period matrix of the Jacobian variety of a curve
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Graduate A question about split short exact sequence
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Graduate What Determines the Degree of the Gauss Map in Differential Geometry?
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Graduate Two cones connected at their vertices do not form a manifold
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Undergrad Why Are Connection 1 Forms Essential in Principal G-Bundles?
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Undergrad How is a manifold locally Euclidean?
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Graduate Metric on ℝ^2 Invariant under Matrix Transformations
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Graduate Oscillating Plane and Z axis - Energy Balance
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Undergrad What does this notation mean? (suffix/prefix on tensors?)
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Graduate Difference between free G-action and effective G-action?
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Undergrad Computing the Weingarten Map L by raising an index
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Graduate How Does the Volume Form on the Unit Sphere Relate to Its Position Vector?
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High School Calculating a straight line within a sphere
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Graduate Why the Chern numbers (integral of Chern class) are integers?
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High School Curve where both x and y approach infinity
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Undergrad Commutator of covariant derivatives
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Undergrad Question About Curvilinear Cooridnates
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Graduate Theory of Surfaces and Theory of Curves Relationship
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Undergrad How do I calculate the surface area of a rotated curve?
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Graduate Differential forms and vector calculus
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Undergrad Meaning of the sign of the geodesic curvature
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Graduate Interior products, exterior derivatives and one forms
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Undergrad Torsion on cylinder described differentially
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Undergrad How to write a Vector Field in Cylindrical Co-ordinates?
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Graduate Torsion forms and particle physics
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Graduate Line integrals of differential forms
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Graduate Definition of the Lie derivative
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Undergrad How are Vectors described in Bispherical Coordinates?
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Graduate Square of the exterior derivative
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Undergrad Prove ∇(A x B) = (∇ x A)⋅B - (∇ x B)⋅A where A,B are vectors
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Graduate Ricci Form Notation: Need Help Understanding
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Graduate Action of a vector on the pull-back of a function
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Undergrad Make a Pseudo-Riemannian Metric Conformal
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Undergrad What shape is the ecliptic as seen from Earth?
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Graduate Unique separation of the vertical and horizontal spaces?
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Undergrad (Index Notation) Summing a product of 3 numbers
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High School Trying to represent a written geometrical description
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High School Deriving the Polar of a Point on a Conic
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Undergrad Levi-Civita: very small problem, need two steps explained
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Undergrad Confusion on Bianchi Identity proof
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Undergrad Lie derivative of a differential form
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Graduate Existence of Complex Structures and Characteristic Classes
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Graduate Maurer–Cartan forms for a matrix group?
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Undergrad Describing position on an ellipse as a function of angle
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Graduate Tangent Bundle questions about commutative diagram
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Undergrad Notation in Spivak's Calculus on Manifolds
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Undergrad Conformal geometry vs. projective geometry
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MHB Finding Distinct and Singular Normals for a Parabola
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Undergrad How directrix for other than parabola?
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MHB First Approach to Differential Forms
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Undergrad Intuition on divergence and curl
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Undergrad Questions about gradient and scalar product
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High School Base space Minkowski, fiber is S^1, total spaces?
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Undergrad Rotation and Translation coordinates
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Undergrad Example of computing geodesics with 2D polar coordinates
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Undergrad Finding shortest distance between skew lines, checking work.
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Undergrad What Is the Geometrical Interpretation of Bounded Curves?
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Undergrad Family of Circles through Two Points: Exists Any Circle Beyond?
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