Bibliography
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@Carinena2023
@KobayashiNomizu1996
@MR2001541
@Morando_mu_variational
@PaolaPfaffian
@Stephani
@arnold1992ordinary
@barcoThesis
@basarab
@berrone2003inverse
@blumanlibro
@bongaartsshort
@bryant2013exterior
@cap2009parabolic
@chicone2006ordinary
@conmorando
@feigin1975characteristic
@fels1999moving
@fels2007integrating
@gaetamorando
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@griffiths1974cartan
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@lawvere2009conceptual
@lee2006riemannian
@lee2013smooth
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@sherring1992geometric
@strocchi2008introduction
@warner
Home
☕REFLECTIONS
4-dimensional spaces
Bell's experiment
Dirac equation
Elliptic, hyperbolic and parabolic geometry
Euclidean plane
Feynman's path integral formulation
Generalization of the flatness of R3
Heisenberg approach to QM
Heisenberg vs Schrodinger picture
Hermitian form, inner product and symplectic form relationship
On Many Worlds, entanglement and hidden variables
On Physics from the beginning
Time zones example
Where is the geometry in a Klein geometry?
Why complex numbers in QM
Why did physics go quantum
about Lie algebras and involutive sets of vector fields
about solvable algebras and solvable structures
bra-ket notation
change of coordinates in quantum mechanics
complex eigenvalues
complexification of a vector space
connection form for LV in R3
connection form for LV in a surface
connections summary
covariance and contravariance in linear algebra
covariance and contravariance on manifolds
curvature like a driving force
double slit experiment
duality in exterior algebras
electromagnetic field
example left invariants vector fields and Maurer-Cartan form
formulation of QM
general covariance and contravariance
integration and derivation
intuition behind tensors
method of moving frames
outline of Galois theory
particle with position and spin
quantum approach to particle motion- an example
relation SO(3) and SU(2)
relation of Lie derivative, covariant derivative and torsion
relation symplectic form and Riemannian metric
relationship parallel transport, covariant derivatives and metrics
several coupled oscillators
states and observables
visualization of Lie groups
♾️ CONCEPTS
ALGEBRA
Galois group
differential ideal
dual vector space
homogeneous space
inverse limit
local ring
localization of a module
localization of a ring
locally free module
normal subgroup
projective module
semidirect product
solvable Lie algebra
solvable group
splitting field
ALGEBRAIC GEOMETRY
locally free O-module
locally free sheaf
presheaf
sheaf
ANALYSIS
Padé aproximant
canonical immersion theorem
canonical submersion theorem
submersion
Banach algebra
Bessel functions
Boltzmann distribution
Boolean algebra
CATEGORY THEORY
adjoint functors
category of sets
category
coproduct in categories
functor
group as a category
groupoid
monoid
product in categories
Cauchy characteristic vector fields
Cauchy complete
Cauchy stress tensor
Cauchy's theorem
Christoffel symbols
Clifford algebra
DEs
Abel equation
Cauchy problem
Cinf_k symmetry
Lie point symmetry
Navier-Stokes equations
ODE
Riccati equation
Schrodinger equation (general family)
Vessiot distribution
characteristics of first-order partial differential equation
first integral
generalized Cinf-symmetry ODE
generalized symmetry of an ODE
generating function
integrating factor
lambda-symmetry
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 ODEs
system of first order linear ODEs- complex case
system of first order linear ODEs- real case
wave equation
DISCRETE DG
2-complex
Discrete Differential Geometry
discrete differential
discrete inmersion
discrete k-form
Dirac delta
Euclidean geometry
Euclidean group
Euler characteristic
Euler operator
Euler-Lagrange
FUNCTIONAL ANALYSIS
Banach space
Hilbert space
inner product space
normed space
Finsler manifold
Fock space
Fourier transform
Frobenius integrable 1-form
G-structure
GEOMETRY
Cartan distribution
Cartan geometry
G-bundle
Gauss map
Gaussian curvature
Hodge star operator
Klein geometry
Levi-Civita connection
Lie algebra
Lie bracket
Lie derivative for tensors in general
Lie derivative of forms
Lie derivative of vector fields
Maurer-Cartan form
Moebius transformations
Pfaffian equation
Pfaffian system
Poincare half plane
Ricci curvature tensor
Riemannian metric
Riemannian volume form
Theorema Egregium
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
differential operator
distribution
embedded manifold
exponential map
extension and reduction of a principal bundle
first fundamental form
foliation
frame bundle
frame on a manifold
functional dependence
fundamental vector field
geodesic
group action
group representation
horizontal cotangent bundle
hyperbolic geometry
immersed manifold
integral submanifold
interior product
involutive distribution
isothermal coordinates
jet bundle
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
pseudo-Riemannian manifold
pseudosphere
second fundamental form
shape operator
solder form
solvable structure
structure 1-form of a distribution
surface
symmetry of a distribution
torsion of a curve
transversal algebra of symmetries
transverse geometry
vector bundle connection
vector field
vertical bundle
Gaussian wave packet
Gelfand spectrum
Geometric Algebra
Grassmannian bundle
Grassmannian manifold
Hamiltonian equations
Hamiltonian group action
Hamiltonian symmetry
Hamiltonian vector field
Hermitian matrix
Hermitian operator
Hessian matrix
Inverse Scattering Method
Jacobi equation
Jacobi field
Jacobi last multiplier
Jordan canonical form of a matrix
Kaluza-Klein theory
Killing vector field
Laplace transform
Laplace's equation
Laplacian operator
Lax pair
Legendre transform
Lie algebra action
Lie group
Lie series
Lipschitz continuous function
Lorentz boost
Lorentz group
Lorentzian manifold
Mellin transform
Minkowski space
Noether symmetry
PDE
Pauli equation
Pauli matrices
Poincare disk
Poincare group
Poisson algebra
Poisson bracket
Poisson manifold
Poisson map
Poisson's equation
Polya vector field
Relativistic Field Theory
Riemann curvature tensor
Riemann normal coordinates
Riemann sphere
Riemann zeta function
Riemannian geometry
Riemannian manifold
SO(3)
SU(2)
Schrodinger equation
Stern-Gerlach experiment
Stokes' theorem
Viviani's theorem
Wronskian
absolute parallelism
affine group
angular momentum
anti-Hermitian operator
automorphism
basis and change of basis
c-star algebra
canonical commutation relations
center of a ring-group
central algebra
centralizer
classical Hamiltonian system
closed map
coherent sheaf
conformal map
conjugate transpose
conservation law
contact transformation
continuity equation
contorsion
contractible space
covariant derivative along a curve
covariant derivative operator
covering group
covering system
curl
curvature of a Cartan geometry
decomposable k-form
derivation in an algebra
determinant
differential function
distribution (functional analysis)
divergence
dynamical system
eigenvalues
eigenvector
emission spectrum
endomorphism
energy of a curve
energy-momentum tensor
entire function
equivalent Lagrangians
evolution equation
evolutionary vector field
exact sequence
excited state
exponential map for Riemannian manifolds
exterior algebra
exterior covariant derivative
exterior derivative
exterior differential system
extrema
extrinsic curvature
f-related vector fields
faithful action
flag of foliations
flag
flow of observables in CM
four-current
four-momentum
free action
gauge theory
general linear group
general relativity theory
generalized momentum
genus
geodesic flow
geodesic polar coordinates
geodesic vector field
geodesically complete manifold
global Gauss-Bonnet theorem
heat equation
holomorphic
holonomic constraint
holonomy
homogeneous ideal
homogeneous linear PDE
induced matrix norm
inhomogeneous linear PDE
inner automorphism
integrable systems
integral of motions
inverse Jacobi multiplier
isometry
lattice
left invariant vector field
left-invariant differential form
length of a curve
local chart connection
local group of transformations
locally compact
mZK equation
manifold
material derivative
matrix algebra
matrix exponential
mean square deviation
method of characteristics
metric space
module
n-volume in an m-dimensional vector space
nonholonomic constraint
nonlocal symmetry
normal topological space
one-parameter subgroup
operator on a normed space
orthogonal and special orthogonal groups
orthogonal matrix
orthonormal frame bundle
paracompact
parallel curves
parallel transport
parallel vector field
parallelizable manifold
particle detector
partition of unity
point transformation
positive functional
pregeodesic vector field
principal bundle morphism
principal direction
principle of least action
projection
projective linear group
projective representation
projective space
propagator
proper action
quadratic form
quantum field
quantum harmonic oscillator
quantum superposition
quasi-linear homogeneous first-order PDEs system
quaternions
quotient action
quotient representation
radical of a Lie algebra
random variable
reductive Cartan geometry
reductive Klein geometry
regular action
regular value
sectional curvature
self adjoint matrix
self adjoint operator
short exact sequence
similarity solution
simple Lie algebra
simple module
skew-symmetric matrix
spectrum of a ring
spin group
spin representation
spinor bundle
spinors
star shaped space
stationary state
stereographic projection
subaction
submanifold
subrepresentation
superintegrable system
symmetric group
symmetric operator
symmetry algebra
symmetry group of a physical system
symmetry of a Pfaffian system
symmetry of an EDS
symplectic form
symplectic group action
symplectic manifold
symplectic vector field
symplectomorphism
system of linear first order homogeneous PDEs
system of linear first order inhomogeneous PDEs
tensor algebra
tensor field
tensor product
tensor
terminal object
time evolution
topos
torsion of a Cartan geometry
torsion of a connection
total derivative operator
total divergence
total vector field
totally-geodesic manifold
trace
transitive action
translation and momentum operators
transport equation
travelling wave solution
uniformly continuous function
unitary matrix
unitary operator
universal enveloping algebra
universal property
variational bicomplex
variational derivative
variational problem
variational symmetry
volume form
von Neumann algebra
wavefunction
wedge product
work and energy
⛳️ NON CLASSIFIED
Abstract Algebra
Analysis
Basic geometry
Classical Field Theory
Classical Mechanics
Classical Statistical Mechanics
Fluid mechanics
Hamiltonian field theory
Hamiltonian mechanics
Koopman-von Neumann classical mechanics
Lagrangian Mechanics
Lagrangian field theory
Linear Algebra
Logic
Noncommutative Geometry
Optics
Penrose abstract index notation
Penrose diagramatic notation
Physics
Quantum Field Theory
Quantum Mechanics
Special Relativity
axiomatic Newtonian mechanics
famous equations
harmonic oscillator
probability theory
raising and lowering indices
✏️ THEOREMS
Baker-Campbell-Hausdorff formula
Banach fixed point theorem
Basarab 1991, proposition 2
Bessel's inequality
Bolzano-Weierstrass theorem
Bäcklund theorem
Cartan lemma
Cartan's first structural equation
Cartan's second structural equation
Cartan-Janet theorem
Cauchy integral formula
Cauchy-Schwarz inequality
Clairaut's theorem
DG
Cartan formula
Frobenius theorem
Harriot theorem
Pithagoras theorem inner product spaces
Serre-Swan theorem
canonical form of a regular vector field
canonical form of commuting vector fields
dual characterization 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 Stokes' theorem
local Gauss-Bonnet theorem
vector bundle-module of section identification
Gauss lemma
Gelfand-Naimark theorem
Godel theorems
Hairy Ball Theorem
Hopf-Rinow theorem
IBD property for vectors
Liouville's formula
MC form for a matrix group
Meusnier's theorem
Minding's theorem
Noether's theorem
Pfaff-Darboux theorem
Plank's law
Poincare lemma
Poincare-Hopf Theorem
Runge-Kutta
Stone's theorem
Stone–Weierstrass theorem
Weierstrass theorem
Zassenhaus formula
bilinear forms diagonalization
block matrix determinant formula
common eigenvectors
commutativity of flows
conservation of momentum
existence of solutions for a system of first order linear inhomogeneous PDEs
extension of a frame
global Frobenius theorem
inverse function theorem
matrix diagonalization
normal subgroup vs ideal of Lie algebra
polar decomposition
preimage theorem
relation between strong and standard symmetries ODE
relation between the determinant and the trace
resolution of identity
singular value decomposition
spectral theory
symmetric matrix
teorema cuadraturas basarab
trigonometric formulas
❓MY RESEARCH
☕REFLECTIONS
Comparison of structures
Fornberg-Whitham equation with cinf-structures
Global vision of solving ODEs
ODE visualization in the two jet bundles
alternative Lie method for first-order ODEs
corank 1 distributions
solution space of an ODE
symmetrizing factors in the case of corank 1
visualization of DE systems
visualization of k-forms
♾️ ❗CONCEPTS
cinf-structure of 1-forms
cinf-structure
cinf-symmetry of distribution
symmetrising factor
✏️❓ CONJECTURES
conjecture_qsolv structure refinada
✏️❗ OWN RESULTS
IBD property for distributions
algorithm for cinf-structures
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
symmetrising factor lemma
✨ IDEAS TO FOLLOW
000 Organization of ideas
Analytic vs geometric reduction
Prolongation formula for Cinf-structures
Riemannian metric for an ODE
Sharma-Tasso-Olver equation with cinf-sructures
about the substitution of the constants
algebraic treatment of cinf-structures
cinf-structure and flags
cinf-structure from non-solvable symmetry algebra
completar una PDE con datos de Cauchy
ideas about JLM
reduction of a distribution by a symmetry
relation Cinf-symmetries distribution with lambda-preservation
sigma-prolongation and cinf-structures
trocear una ODE orden m