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 Infinitesimal Movement Along 3-d Geodesics
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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 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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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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High School Is my intuitive way of thinking about non-Euclidean geometry valid?
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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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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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Undergrad Differential Geometry: Comparing Metric Tensors
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High School Question about Mercator's projection
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High School What Does the Scalar R Represent in Tensor Mapping on a Smooth Manifold?
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High School What makes pressure a tensor quantity?
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Undergrad Computing the Directional Derivative ....
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Undergrad Deriving the area of a spherical triangle from the metric
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Graduate Covariant derivative and connection of a covector field
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Undergrad How Do Lie Derivatives Connect to Symmetry and Conservation Laws in Physics?
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Undergrad Geodesics subject to a restriction
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Undergrad The vanishing of the covariant derivative of the metric tensor
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Undergrad Equivalent paths to the Christoffel symbols
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Undergrad Curve Inside a Sphere: Differentiating Alpha
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Undergrad Christoffel symbols and covariant derivative intuition
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Graduate Connection between 1-Forms and Fourier Transform
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High School How to know if a Euclidean space is not a 3-sphere?
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Undergrad Defining a Point on a Manifold: Intrinsic vs Embedded Space
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Undergrad Is a Full-Cone in E^3 a Topological Manifold?
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Undergrad Invariant properties of metric tensor
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Undergrad "Adding" a Vector Space and its Dual
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Graduate Is the Berry connection a Levi-Civita connection?
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Undergrad Question about geodesics on a sphere
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Undergrad Circumference of a circle on a spherical surface
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Undergrad Using the derivative of a tangent vector to define a geodesic
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Undergrad Aristotle's Absolute Space & Time: Explained
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Undergrad Understanding the definition of derivative
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Undergrad What is the Purpose of Calculating the Christoffel Symbols in Curved Spacetime?
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Undergrad Vector valued integrals in the theory of differential forms
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Undergrad Can the area be understood as the "number of points"?
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Graduate Why the terms - exterior, closed, exact?
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Undergrad Question about a partial derivative
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Graduate I need some fun questions with answers in differential geometry ()
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Undergrad Trying to construct a particular manifold locally using a metric
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Undergrad Derivative of the Ad map on a Lie group
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Undergrad Understanding vector differential
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Graduate Two Covariant Derivatives (Chain Rule)?
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Undergrad Geodesics under coordinate transformation
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Undergrad About the definition of a Manifold
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Undergrad Larger assignment on Vector Fields
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Graduate Can anyone alive derive these quaternion equations?
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Undergrad Difference (if any) between E^1 x E^3 and E^4
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Graduate Is the Exponential Map Always Surjective from Lie Algebras to Lie Groups?
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Undergrad Diffeomorphism invariance and contracted Bianchi identity
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Undergrad Bases for Tangent Spaces and Subspaces - McInerney Theorem 3.3.14
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Undergrad Algorithm to determine the roulette curve
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Minimal Surfaces, Differential Geometry, and Partial Differential Equations
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Undergrad Parameterized surfaces from coordinates
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Graduate Defining the Tensor Product of Gradients for Different Coordinate Systems
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Graduate Transversality unlocks the secrets of the manifold?
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Undergrad Proving that an action is transitive in the orbits
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Graduate Fractional spacetime, dimension equation
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Undergrad Uncovering the Derivative of a Tensor: Understanding its Equations and Origins
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Graduate Equivalence of diffeomorphism definitions
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Graduate Logical foundations of smooth manifolds
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High School Are Polar Coordinates on ##\mathbb R^2## a Coordinate System?
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Undergrad Coordinate systems on the 2-sphere
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Graduate Second order partial derivatives vanish?
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Graduate Question about covariant derivatives
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Undergrad Set of possible rotations of a 3D object and the rotation history
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