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 Coordinates in geometry
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B Curvature and geodesics
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I What is an (almost) complex manifold in simple words
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I Infinitesimal Movement Along 3-d Geodesics
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A Parallel transport on a symplectic space
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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
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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 Implicitly differentiating the vanishing real part of the hyperbolic tangent of one plus the square of the Hardy Z function
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B Torsion tensor definition doubt
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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 Understanding Kahler Manifolds
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I About Covariant Derivative as a tensor
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I Maximally Symmetric 3-Spaces
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I Galilean spacetime as a fiber bundle
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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 Möbius strip as fiber bundle
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A Connections and distributions
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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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I Component definition in curvilinear coordinates
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B Question about Mercator's projection
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B What is this Tensor mapping to?
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B What is 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 Lie Derivatives and Symmetry
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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
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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 Point on a manifold
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I Full-cone as topological space
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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 Maxwell's equations with differential forms
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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 Why absolute space cannot be represented as fibers on the axis the absolute time?
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I Understanding the definition of derivative
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I Metric tensor derivatives
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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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A High Dimensional Geometry of Brain Representations
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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 Lie Algebra and Lie Group
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I Variation of geometrical quantities under infinitesimal deformation
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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 Tensor product of gradients
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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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Differential Geometry

Welcome to the Differential Geometry forum!

Join experts in discussing differential geometry topics. This includes manifolds, Tensors and forms. Connections and curvature also.

Properties and fundamental geometric invariants of curves and surfaces in space; applications to the physical sciences. Pre: Calculus IV, and Introduction to Linear Algebra; or consent.

Differential and algebraic topology discussion. Homework help is available in the homework forums.

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