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.
On covariance of the Lagrange equations
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I Differential Geometry with GNU/Linux
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A Injective immersion and embedding
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I Get geodesics & parallel transport on 2D surfaces (discrete timestep)
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I Compact manifold cannot be represented by (single) parametric equation
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I Do non-orthogonal coordinate systems mean dependent coordinates?
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I ##C^{\infty}##-module of smooth vector fields can lack a basis
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I Round 3-sphere symmetries as subspace of 4D Euclidean space
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I Differential structures over a topological manifold
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I ##SO(3)## topology
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I Pseudo-Riemaniann isometries
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I Spherically symmetric manifold
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I Smooth Manifold Chart Lemma
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I Vector fields wedge product vs covector field
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I Definition of a Manifold
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I Chain Rule (partial derivatives): basic interpretation question
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I Definition of inertia tensor from a differential geometry viewpoint
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I Closed implies exact (differential 1-forms on R^2)
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I Transformation of second rank tensor
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I Differential structure on topological manifolds of dimension <= 3
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I Maximal atlas of topological manifold
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I Galilean spacetime as a fiber bundle
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I 2-sphere with any topology can't be homeomorphic to the plane
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I Must a Smooth Section Over a Mobius Strip Take Value Zero at Some Point?
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I Properties of the initial topology from a topological manifold
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A Bachman : A geometric approach to differential forms
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I Poincare lemma for one-form on ##\mathbb R^2 \backslash \{ 0 \}##
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B Axes on a hyperbolic plane
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I On the definition of canonical coordinates in phase space
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I Confused about the inner product
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I Induced metric in general case
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I Dot product between basis vectors and dual basis vectors
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Is the Lie derivative a tensor itself?
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I Is there a consensus about the meaning of the Christoffel symbols' indices?
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I Inner product of two tensors
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I Question about Gradient's Domain and Range
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A Understanding: double of conformally flat manifold is conformally flat
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I How to find inverse coordinates?
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I The Road to Reality - exercise on scalar product
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I Trying to learn tensor algebra
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I Notion of congruent curve along a vector field
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I Dirichlet problem boundary conditions
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I Which basis-forms are pseudo-tensors?
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A Alternative topology of our 3D space
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I Manifold hypersurface foliation and Frobenius theorem
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I SL(n,R) Lie group as submanifold of GL(n,R)
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I Grassmannian as smooth manifold
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I Can covariant derivative tensorialness be derived?
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I Frobenius theorem applied to frame fields
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I 2-sphere manifold intrinsic definition
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I Radius of curvature formula when the denominator = 0
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I Quotient law and the curl in index notation
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I What is the difference between Gaussian and sectional curvature?
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I Do gradient and curl only differ by a Levi-Cavita tensor?
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B Hopf fibration, Bloch sphere and quantum rotations - interactive site
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I 3-parameter group of symmetries on the plane
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I Approximating smooth curved manifolds with "local bits" of curvature?
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I Conformal flatness of ellipsoid
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I Definition of manifolds with boundary
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I When can I commute the 4-gradient and the "space-time" integral?
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I Identification tangent bundle over affine space with product bundle
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I Induced orientation on boundary of ##\mathbb{H}^n## in ##\mathbb{R}^n##
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I Resources on the Derivation of generalized Stokes' theorem
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A How to switch from tensor products to wedge product
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I Is Diagrammatic Tensor Notation Widely Used in Mathematics?
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A 3-connection on nontrivial topological 3-manifold
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I Question regarding the 3-form ##dx^i \wedge dx^j \wedge dx^k##
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I Short question about principal bundle
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I Definition of tangent vector on smooth manifold
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I How to apply tensor transformation rule
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A What subset of a 3D space can be addressed by a single chart?
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I Frobenius theorem for differential one forms
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I Dirac delta function in 2d polar coordinates
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A Differential structure of the group of automorphism of a Lie group
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I Invariance of a tensor of order 2
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A What Is the Gauss Embedding Theorem Mentioned in the Video Talk?
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I Help with Differential Forms - self wedge product terms
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I Rewriting Equation of Motion in terms of Dual Fields (Chern-Simons)
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I Contact manifold and Darboux's theorem
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I Differential operator vs one-form (covector field)
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B East-West error at regular points on the Azimuthal Equidistant Map
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I How do I parametrize a conical/cylindrical surface in cylindrical unit vectors?
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I How can a sphere be transformed using differential geometry?
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I Miller indices and periodic boundary conditions
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I Trouble with metric. Holonomic basis and the normalised basis
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A Tensor/Vector decomposition/representation & DOF arguement
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I What does a complex vector "look" like?
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A Problems with the interpretation of the Torsion tensor and the Lie Bracket
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I What is Riemann's approach to classifying 2d surfaces?
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I Parallel Transport Along Geodesic
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A A claim about smooth maps between smooth manifolds
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A Calculate a tensor as the sum of gradients and compute a surface integral
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A Hodge operator on 4th rank tensor
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I First algebraic Bianchi identity of Riemann tensor (cyclic relation)
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I What is the Trace of a Fourth Rank Tensor in Index Notation?
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A Newmann-Penrose Spin coefficients for Schwarschild metric
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A In what representation do Dirac adjoint spinors lie?
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I Do diffeomorphisms have to be one-to-one functions?
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About lie algebras, vector fields and derivations
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A Hodge decomposition of a 1-form on a torus
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