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.
B Understanding 3D Temperature Direction Change with 8 Corner Points
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A Exists ? : Invariant geodesic equation
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B Increasing the dimensions of a manifold
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I Why Torsion = 0 => Planar Curve in this Proof
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I Fixing an orientation for a connected smooth surface
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B Relating basis vectors at different points in a neighborhood
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B Standard version of covariant derivative properties
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B Defining the derivative of a vector field component
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I Product Space vs Fiber Bundle: Understanding the Difference
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I The second fundamental form and derived metrics
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A Can we always rewrite a Tensor as a differential form?
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A How Can I Differentiate Curves Where the Real Part of \( Y(t) \) Vanishes?
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B Why is There No Factor of 1/2 in the Torsion Tensor Definition?
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B Solving for integral curves- how to account for changing charts?
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B Reconciling basis vector operators with partial derivative operators
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I Tangent space basis vectors under a coordinate change
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B Derivative of a constant scalar field at a point
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I Sachs and Wu's General Relativity for Mathematicians
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I Directional Derivatives of a vector ----gradient of f(P)----
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A What Is a Kahler Manifold?
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I About Covariant Derivative as a tensor
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I Understanding the Definition of Isotropic Spaces in Riemannian Manifolds
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B Is my intuitive way of thinking about non-Euclidean geometry valid?
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I Visualizing the cotangent space to a sphere
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I How Do Transition Functions Define a Möbius Strip in Fiber Bundles?
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A Are there references and do the converse theorems hold for theorems 1,2?
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A Diffeomorphic manifolds of equal constant curvature
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A Question about the derivation of the tangent vector on a manifold
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A Simple question on the derivative of base frame
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A Geodesics of the 2-sphere in terms of the arc length
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I Sufficient condition for a vector field to be conservative
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I Living inside a Hopf fibration, seeing the fibers
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I Beltrami flows have zero parallel gradients?
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I Geodesics on a sphere and the Christoffel symbols
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B An intrinsic equation of a surface
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I A set of numbers as a smooth curved changing manifold.
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A Pullback of the metric from R3 to S2
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A Differential movement along a curved surface
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I Question on tangent space and jet spaces
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B Dilating or expanding a closed ball in Riemannian geometry
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I Differential Geometry: Comparing Metric Tensors
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B Question about Mercator's projection
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B What Does the Scalar R Represent in Tensor Mapping on a Smooth Manifold?
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B What makes pressure a tensor quantity?
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I Computing the Directional Derivative ....
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I Deriving the area of a spherical triangle from the metric
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A Covariant derivative and connection of a covector field
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I How Do Lie Derivatives Connect to Symmetry and Conservation Laws in Physics?
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I Geodesics subject to a restriction
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I The vanishing of the covariant derivative of the metric tensor
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I Equivalent paths to the Christoffel symbols
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I Curve Inside a Sphere: Differentiating Alpha
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I Christoffel symbols and covariant derivative intuition
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A Connection between 1-Forms and Fourier Transform
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B How to know if a Euclidean space is not a 3-sphere?
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I Defining a Point on a Manifold: Intrinsic vs Embedded Space
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I Is a Full-Cone in E^3 a Topological Manifold?
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I Invariant properties of metric tensor
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I "Adding" a Vector Space and its Dual
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A Is the Berry connection a Levi-Civita connection?
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I Question about geodesics on a sphere
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I Circumference of a circle on a spherical surface
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I Using the derivative of a tangent vector to define a geodesic
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I Aristotle's Absolute Space & Time: Explained
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I Understanding the definition of derivative
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I What is the Purpose of Calculating the Christoffel Symbols in Curved Spacetime?
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I Vector valued integrals in the theory of differential forms
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I Can the area be understood as the "number of points"?
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A Why the terms - exterior, closed, exact?
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I Question about a partial derivative
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A I need some fun questions with answers in differential geometry ()
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I Trying to construct a particular manifold locally using a metric
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I Derivative of the Ad map on a Lie group
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I Understanding vector differential
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A Two Covariant Derivatives (Chain Rule)?
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I Geodesics under coordinate transformation
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I About the definition of a Manifold
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I Larger assignment on Vector Fields
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A Can anyone alive derive these quaternion equations?
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I Difference (if any) between E^1 x E^3 and E^4
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A Is the Exponential Map Always Surjective from Lie Algebras to Lie Groups?
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I Diffeomorphism invariance and contracted Bianchi identity
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I Bases for Tangent Spaces and Subspaces - McInerney Theorem 3.3.14
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I Algorithm to determine the roulette curve
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Minimal Surfaces, Differential Geometry, and Partial Differential Equations
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I Parameterized surfaces from coordinates
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A Defining the Tensor Product of Gradients for Different Coordinate Systems
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A Transversality unlocks the secrets of the manifold?
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I Proving that an action is transitive in the orbits
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A Fractional spacetime, dimension equation
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I Uncovering the Derivative of a Tensor: Understanding its Equations and Origins
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A Equivalence of diffeomorphism definitions
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A Logical foundations of smooth manifolds
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B Are Polar Coordinates on ##\mathbb R^2## a Coordinate System?
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I Coordinate systems on the 2-sphere
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A Second order partial derivatives vanish?
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A Question about covariant derivatives
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I Set of possible rotations of a 3D object and the rotation history
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I Is There a Generalized Fourier Transform for All Manifolds?
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I Deriving the spherical volume element
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