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.
Graduate Hilbert spaces and kets "over" manifolds
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Undergrad Trouble understanding contravariant transformations for vectors
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Undergrad Vector squared in polar coordinates
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Graduate What is the geometric approach to mathematical research?
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Undergrad Math Myth: The sum of all angles in a triangle is 180°
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Graduate Help requested with translating math into code (Not homework)
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Graduate Differential forms on R^n vs. on manifold
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Undergrad Understanding Geodesic Parametrization on a Sphere
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Graduate On the relationship between Chern number and zeros of a section
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Undergrad Definition of tangent space: why germs?
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Undergrad Transition Functions and Lie Groups
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Undergrad Is There a Distinction Between Riemann Metrics in Physics?
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High School Ways to abstract curves or surfaces
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Graduate Lagrangian for straight line in XY-plane (dependent on time)
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Graduate Why are sheafs defined using abelian groups?
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Graduate Something about configuration manifolds in classical mechanics
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Graduate Connection between Reciprocal Space and Cotangent Space
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Graduate On the different ways of determining curvature on manifolds
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Graduate Information Geometry: Is there any there there?
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Undergrad What are the restrictions when swapping between geometries in physics?
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Undergrad Tensor rank: One number or two?
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Undergrad Pushforward/Pullback of Vector Field
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Graduate Transformation of coordinate basis
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High School Examples of manifolds not being groups
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Graduate Natural parametrization of a curve
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Undergrad Position of a point as a function of angular position
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Undergrad About divergence, gradient and thermodynamics
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Graduate What is the Concept of Spectral Geometry?
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Undergrad Integration of differential forms
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Undergrad Parallel transport on flat space
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Undergrad Closest point on a plane to a point near the plane
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Undergrad Testing my knowledge of differential forms
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Undergrad Can Topological Spaces Have Properties Similar to Manifolds?
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Undergrad Prove the following statement about n-Manifolds
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Undergrad What is the Minkowski metric tensor's trace?
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Undergrad Finding the change in position and angle after moving the rectangle
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Graduate What is a Fibre Bundle? A 5 Minute Introduction
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MHB Discrete Geometry: Info, Knowledge & More
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Undergrad Covariant derivatives, connections, metrics, and Christoffel symbols
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Undergrad Derived metrics on surfaces of positive curvature
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Undergrad Difference between diffeomorphism and homeomorphism
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Undergrad Fixing orientation by fixing a frame in a tangent space
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Undergrad Riemannian Fisher-Rao metric and orthogonal parameter space
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Undergrad How is this a representation of a 3 dimensional torus?
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High School Can coordinates be functions in geometry?
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High School Can Curvature and Geodesics be Generalized in Higher Dimensions?
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Undergrad What is an (almost) complex manifold in simple words
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Undergrad Is a vector itself contra/covariant or just its components?
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High School Why does the Wikipedia article use a negative sign in the 4-gradient?
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MHB How do I find the Euclidean Coordinate Functions of a parametrized curve?
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Undergrad Infinitesimal Movement Along 3-d Geodesics
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Undergrad Elliptic Function Rotation Problem
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Undergrad Geometry and algebraic equations
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Graduate Parallel transport on a symplectic space
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High School Understanding 3D Temperature Direction Change with 8 Corner Points
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Graduate Exists ? : Invariant geodesic equation
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High School Increasing the dimensions of a manifold
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Undergrad Why Torsion = 0 => Planar Curve in this Proof
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Undergrad Fixing an orientation for a connected smooth surface
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High School Relating basis vectors at different points in a neighborhood
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High School Standard version of covariant derivative properties
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High School Defining the derivative of a vector field component
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Undergrad Product Space vs Fiber Bundle: Understanding the Difference
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Undergrad The second fundamental form and derived metrics
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Graduate Can we always rewrite a Tensor as a differential form?
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Graduate How Can I Differentiate Curves Where the Real Part of \( Y(t) \) Vanishes?
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High School Why is There No Factor of 1/2 in the Torsion Tensor Definition?
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High School Solving for integral curves- how to account for changing charts?
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High School Reconciling basis vector operators with partial derivative operators
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Undergrad Tangent space basis vectors under a coordinate change
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High School Derivative of a constant scalar field at a point
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Undergrad Partial Surface Area of a Tube
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Undergrad Area of an inclined surface with respect to the original surface
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Undergrad Sachs and Wu's General Relativity for Mathematicians
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Undergrad Directional Derivatives of a vector ----gradient of f(P)----
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Graduate What Is a Kahler Manifold?
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High School A covariant vs contravariant vector?
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Undergrad About Covariant Derivative as a tensor
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Undergrad Understanding the Definition of Isotropic Spaces in Riemannian Manifolds
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Undergrad Differentiating the Dot Product's Evil Twin
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High School Is my intuitive way of thinking about non-Euclidean geometry valid?
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Graduate How to understand when surface terms go to zero
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Undergrad Visualizing the cotangent space to a sphere
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Undergrad How Do Transition Functions Define a Möbius Strip in Fiber Bundles?
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Graduate Are there references and do the converse theorems hold for theorems 1,2?
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Graduate Diffeomorphic manifolds of equal constant curvature
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MHB Where Do These Parametric Equations and Plane Intersect?
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Graduate Question about the derivation of the tangent vector on a manifold
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Graduate Simple question on the derivative of base frame
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Graduate Geodesics of the 2-sphere in terms of the arc length
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Undergrad Sufficient condition for a vector field to be conservative
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Undergrad Living inside a Hopf fibration, seeing the fibers
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Undergrad Beltrami flows have zero parallel gradients?
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Undergrad Geodesics on a sphere and the Christoffel symbols
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High School An intrinsic equation of a surface
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Undergrad A set of numbers as a smooth curved changing manifold.
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Graduate Pullback of the metric from R3 to S2
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Graduate Differential movement along a curved surface
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Undergrad Question on tangent space and jet spaces
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High School Dilating or expanding a closed ball in Riemannian geometry
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