Acabo de crear un nuevo blog. Se llama "What I have learned today". En él pretendo incluir todas mis anotaciones de física y matemáticas (totalmente informales) por si pudieran servir de algo a alguien.
La dirección es
- Home
- ☕REFLECTIONS
- Elliptic, hyperbolic and parabolic geometry
- about Lie algebras and involutive sets of vector fields
- about solvable algebras and solvable structures
- connections summary
- curvature like a driving force
- outline of Galois theory
- visualization of 1-forms
- ♾️ CONCEPTS
- ALGEBRA
- Galois group
- differential ideal
- dual vector space
- homogeneous space
- inverse limit
- locally free module
- normal subgroup
- projective module
- semidirect product
- solvable Lie algebra
- solvable group
- splitting field
- ALGEBRAIC GEOMETRY
- ANALYSIS
- CATEGORY THEORY
- adjoint functors
- category of sets
- category
- coproduct (cat th)
- functor
- group (and category theory)
- groupoid
- monoid
- product (cat th)
- DEs
- Cinf_k symmetry
- Lie point symmetry
- ODE
- Vessiot distribution
- characteristics of first-order partial differential equation
- dynamical Cinf-symmetry ODE
- dynamical symmetry de ODE
- first integral
- integrating factor
- lambdasymmetry
- prolongation formula for vector fields
- prolongation of a diffeomorphism
- quadrature
- strong symmetry
- symmetry group of a DE system
- system of DEs
- system of ODEs
- system of first order differential equations
- FUNCTIONAL ANALYSIS
- G-structure
- GEOMETRY
- (pseudo)-Riemannian manifold
- Cartan distribution
- Cartan geometry
- G-bundle
- Gauss map
- Gaussian curvature
- Klein geometry
- Levi-Civita connection
- Lie algebra
- Lie bracket
- Lie derivative of vector fields
- Maurer-Cartan form
- Moebius transformations
- Pfaffian equation
- Pfaffian system
- Poincare half plane
- Riemannian metric
- Weingarten map
- adjoint representation
- associated bundle
- associated connection
- bundle
- coframe on a manifold
- commutator subalgebra
- completely integrable distribution
- completely non-integrable
- connection on a fiber bundle
- cross section
- curvature of a connection
- curvature of a curve
- curvature of a distribution
- distribution
- embedded manifold
- exponential map
- extension and restriction of principal bundles
- first fundamental form
- foliation
- frame bundle
- frame on a manifold
- functional dependence
- fundamental vector field
- geodesic curve
- group action
- group representation
- horizontal cotangent bundle
- hyperbolic geometry
- immersed manifold
- integral submanifold
- involutive distribution
- isothermal coordinates
- jet space
- linear connection
- moving frame
- normal and geodesic curvature of a curve
- normal curvature of an immersed surface
- orbifold
- principal bundle
- principal connection on a principal bundle
- principal curvatures
- projectable vector field
- prolongation of a section
- pseudosphere
- second fundamental form
- shape operator
- solder form
- solvable structure
- structure 1-form of a distribution
- surface
- symmetry of distribution
- torsion of a curve
- transversal algebra of symmetries
- transverse geometry
- vector bundle connection
- vector field
- vertical bundle
- LINEAR ALGEBRA
- Lie algebra action
- Lie group
- Lorentz group
- Minkowski space
- PHYSICS
- Poincare disk
- Poincare group
- Riemann sphere
- contractible
- flag
- normal topological space
- parallelizable manifold
- ⛳️ NON CLASSIFIED
- ✏️ THEOREMS
- Cartan lemma
- DG
- Cartan formula
- Frobenius theorem
- Serre-Swan theorem
- canonical form of a regular vector field
- canonical form of commuting vector fields
- dual charaterization involutiveness
- dual description of the distribution
- flow of the sum of two vector fields
- flow theorem for vector fields
- formulas for Lie derivative, exterior derivatives, bracket, interior product
- infinitesimal Stoke's theorem
- local Gauss-Bonnet theorem
- vector bundle-module of section identification
- Meusnier's theorem
- completion of a frame
- normal subgroup vs ideal of Lie algebra
- relation between strong and standard symmetries ODE
- teorema cuadraturas basarab
- ❓MY RESEARCH
- ☕REFLECTIONS ✨ IDEAS TO FOLLOW
- ♾️ ❗CONCEPTS
- ✏️❓ CONJECTURES
- ✏️❗ OWN RESULTS
- about the substitution of the constants
- equivalence of cinf-sym and qsolv str in second order
- int_factor vs sym _function relationship
- integrability by Pfaffian equations
- lemma of belongingness to ideal
- método atrás-adelante
- prolongation formula for dynamical Cinf-symmetries
- symmetrizing factor lemma
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