tom · @tomcuchta
112 followers · 202 posts · Server mathstodon.xyz
From "Fundamentals of Differential Geometry" by S. Lang (1999)
https://link.springer.com/book/10.1007/978-1-4612-0541-8?utm_source=dlvr.it&utm_medium=mastodon
Erwin Schrödinger Institute · @ESIVienna
124 followers · 64 posts · Server mathstodon.xyzHave you seen the latest article from our workshop (non-regular #spacetime #geometry) participants? 👉
Saúl Burgos, José Luis Flores and Jónatan Herrera: The c-completion of Lorentzian metric spaces
#SpacetimeGeometry
#DifferentialGeometry #GeneralRelativity #QuantumCosmology #MathematicalPhysics #Quantum #Cosmology #Relativity #MetricGeometry
@univienna
https://arxiv.org/pdf/2305.02004.pdf
(for the motion picture please visit https://twitter.com/ESIVienna/status/1671167715313344512)
#metricgeometry #relativity #cosmology #quantum #mathematicalphysics #quantumcosmology #generalrelativity #differentialgeometry #spacetimegeometry #geometry #spacetime
Erwin Schrödinger Institute · @ESIVienna
119 followers · 57 posts · Server mathstodon.xyz
Have you seen the latest article by Brian Allen, a former workshop participant?
#Spacetime #Geometry #SpacetimeGeometry
#DifferentialGeometry #GeneralRelativity #QuantumCosmology #MathematicalPhysics #Quantum #Cosmology #Relativity #MetricGeometry
@univienna
#metricgeometry #relativity #cosmology #quantum #mathematicalphysics #quantumcosmology #generalrelativity #differentialgeometry #spacetimegeometry #geometry #spacetime
Seth Axen 🪓 :julia: 🦖 · @sethaxen
712 followers · 483 posts · Server bayes.clubI've worked out that the injectivity radius under the Euclidean metric for the #unitary group U(n) is π and for real and special subgroups O(n), SO(n), and SU(n) is π√2.
This seems like a pretty basic property, but I can't find a single reference that gives the injectivity radii for any of these groups. Anyone know of one?
#unitary #differentialgeometry #liegroups #manifolds
Pustam Raut🇳🇵(पुस्तम राउत) · @pustam_egr
43 followers · 130 posts · Server mathstodon.xyz
"Riemann’s Seminal Lecture on Non-Euclidean Geometry" by Areeba Merriam 👉 🔗 https://www.cantorsparadise.com/reimanns-seminal-lecture-on-non-euclidean-geometry-11673a8d6fbb
#Riemann #SeminalLecture #NonEuclideanGeometry #EuclideanGeometry #Gravity #DifferentialGeometry #Relativity #GeneralRelativity #SpecialRelativity #RiemannianGeometry #Tensor #Minkowski #HermannMinkowski #Spacetime #Space #Time #Curvature #Klein #Jacobi #Dirichlet #Gauss #Hypersurface #EllipticGeometry #Geometry #Physics #Topology #Hyperspace #Einstein #AlbertEinstein #Isaacson #MichioKaku #Kaku
#Kaku #michiokaku #isaacson #alberteinstein #einstein #hyperspace #topology #physics #geometry #ellipticgeometry #hypersurface #gauss #dirichlet #jacobi #klein #curvature #time #space #spacetime #hermannminkowski #minkowski #tensor #riemanniangeometry #specialrelativity #generalrelativity #relativity #differentialgeometry #gravity #EuclideanGeometry #NoneuclideanGeometry #seminallecture #riemann
Pustam Raut🇳🇵(पुस्तम राउत) · @pustam_egr
33 followers · 109 posts · Server mathstodon.xyzGENERALIZED STOKES THEOREM:
The integral of a differential form \(\omega\) over the boundary \(\partial\Omega\) of some orientable manifold \(\Omega\) is equal to the integral of its exterior derivative \(d\omega\) over the whole of \(\Omega\).
\[\displaystyle\int_{\partial\Omega}\omega=\int_\Omega d\omega\]
#VectorCalculus #DifferentialGeometry #MultivariateCalculus #Calculus #StokesTheorem #GeneralizedStokesTheorem #Calculus #FundamentalTheorem #Manifold #Boundary #ExteriorDerivative #Stokes
#Stokes #exteriorderivative #boundary #manifold #fundamentaltheorem #generalizedstokestheorem #stokestheorem #calculus #multivariatecalculus #differentialgeometry #vectorcalculus
Pustam Raut🇳🇵(पुस्तम राउत) · @pustam_egr
33 followers · 109 posts · Server mathstodon.xyzGENERALIZED STOKES THEOREM:
The integral of a differential form \(\omega\) over the boundary \(\partial\Omega\) of some orientable manifold \(\Omega\) is equal to the integral of its exterior derivative \(d\omega\) over the whole of \(\Omega\).
\[\displaystyle\int_{\partial\Omega}\omega=\int_\Omega d\omega\]
#VectorCalculus #DifferentialGeometry #MultivariateCalculus #Calculus #StokesTheorem #GeneralizedStokesTheorem #Calculus #FundamentalTheorem #Manifold #Boundary #ExteriorDerivative #Stokes
#Stokes #exteriorderivative #boundary #manifold #fundamentaltheorem #generalizedstokestheorem #stokestheorem #calculus #multivariatecalculus #differentialgeometry #vectorcalculus
Pustam Raut🇳🇵(पुस्तम राउत) · @pustam_egr
33 followers · 109 posts · Server mathstodon.xyzGENERALIZED STOKES THEOREM:
The integral of a differential form \(\omega\) over the boundary \(\partial\Omega\) of some orientable manifold \(\Omega\) is equal to the integral of its exterior derivative \(d\omega\) over the whole of \(\Omega\).
\[\displaystyle\int_{\partial\Omega}\omega=\int_\Omega d\omega\]
#VectorCalculus #DifferentialGeometry #MultivariateCalculus #Calculus #StokesTheorem #GeneralizedStokesTheorem #Calculus #FundamentalTheorem #Manifold #Boundary #ExteriorDerivative #Stokes
#Stokes #exteriorderivative #boundary #manifold #fundamentaltheorem #generalizedstokestheorem #stokestheorem #calculus #multivariatecalculus #differentialgeometry #vectorcalculus
Björn Gohla · @6d03
48 followers · 649 posts · Server mathstodon.xyzConjecture: Monoids in the category of smooth manifolds are groups.
Conjecture: A monoid in the category of smooth manifolds with boundary has non-invertible elements iff the boundary is non-empty. In that case the boundary is the maximal subgroup; in particular, the monoid unit lies on the boundary.
#showerthought #differentialgeometry
Pustam Raut🇳🇵(पुस्तम राउत) · @pustam_egr
25 followers · 74 posts · Server mathstodon.xyzSpacetime is a four-dimensional topological manifold with a smooth atlas carrying a torsion-free connection compatible with a Lorentzian metric and a time orientation satisfying the Einstein field equations (EFE).
\[\underbrace{(\mathcal{M},\mathcal{O},\mathcal{A},\nabla,\text{g},\mathcal{T})}_{\text{Relativistic spacetime}}\]
#spacetime #space #time #physics #relativity #generalrelativity #specialrelativity #differentialgeometry #manifold #theoreticalphysics #einstein #lorentz
#Lorentz #einstein #theoreticalphysics #manifold #differentialgeometry #specialrelativity #generalrelativity #relativity #physics #time #space #spacetime
Pustam Raut🇳🇵(पुस्तम राउत) · @pustam_egr
19 followers · 63 posts · Server mathstodon.xyzGeodesic equation using Einstein summation convention:
\[\boxed{\ddot{\gamma}^\mu+\Gamma^\mu_{\alpha\beta}\dot\gamma^\alpha\dot\gamma^\beta=0}\]
which are the Euler-Lagrange equations of motion for the energy functional, and \(\Gamma^\mu_{\alpha\beta}\) are the Christoffel symbols. In general relativity, a geodesic generalizes the notion of a "straight line" to curved spacetime. #generalrelativity #spacetime #mathematicalphysics #geodesic #differentialgeometry #physics #differentialequations
#differentialequations #physics #differentialgeometry #geodesic #mathematicalphysics #spacetime #generalrelativity
· @j_bertolotti
1301 followers · 341 posts · Server mathstodon.xyz#PhysicsFactlet
Field lines are a convenient way to visualize vector fields, and are defined to be tangent to them at each point.
Due to inertia, field lines do not represent the trajectory that a test mass would follow in a force field.
#VectorFields #DifferentialGeometry #Visualization
#visualization #differentialgeometry #vectorfields #physicsfactlet
Applied Geometry Lab · @appliedgeometry
12 followers · 7 posts · Server sigmoid.social
Applied Geometry Lab · @appliedgeometry
10 followers · 6 posts · Server sigmoid.social
Quiet_Guy · @quiet
37 followers · 146 posts · Server infosec.exchangeHas it ever bothered any of you #math nerds that in #DifferentialGeometry "normal" and "tangent" mean the opposite of their use outside of math?
Rhetorically, a tangent is a digression and an orthogonal concept isn't normal.
#math #differentialgeometry #randomthoughts
Ulises Rayon · @uncrayon
0 followers · 1 posts · Server masto.esWhat's the best textbook on Differential Geometry for undergraduates?
#math #undergraduates #differentialgeometry #geometry
latent-variable · @bobflagg
11 followers · 4 posts · Server mathstodon.xyz
Just got an early Christmas gift! #optimization, #informationgeometry, #differentialgeometry
#differentialgeometry #InformationGeometry #optimization
SciHi Blog · @scihiblog
117 followers · 28 posts · Server fedihum.orgOn December 8, 1865, French mathematician Jacques Salomon Hadamard was born. Hadamard made major contributions in number theory, complex function theory, differential geometry and partial differential equations. Moreover, he is also known for his description of the mathematical though process in his book Psychology of Invention in the Mathematical Field.
http://scihi.org/jacques-hadamard/
#maths #historyofscience #otd #numbertheory #differentialgeometry
#complexfunction
#maths #historyofscience #otd #numbertheory #differentialgeometry #complexfunction
Jon Awbrey · @Inquiry
85 followers · 291 posts · Server mathstodon.xyzHi Charlotte,
I think a lot about analogies between #Logic and physics, or #SystemsTheory more generally. This led me to see the need for the “missing grape” of #DifferentialLogic analogous to #DifferentialGeometry. A lot of it amounts to differential geometry over \(\mathbb{B} = \mathbb{F}_2 = \mathrm{GF}(2)\) and of course Char 2 makes things a little bit weird and degenerate to a degree but it can be worked out.
#differentialgeometry #DifferentialLogic #systemstheory #logic
Junghyeon Park · @j824h
162 followers · 341 posts · Server mathstodon.xyz
@mrdk @narain On the other hand, a parallelogram in the etymological sense, both pair of opposite edges being parallel (their tangents in a parallel transport by other two lines?), is broken as soon as non-zero Riemann curvature is introduced.
In that sense, we might instead want something like a quadrilateral with as many parallel edges as possible. Turns out such shapes have a name.
https://en.m.wikipedia.org/wiki/Levi-Civita_parallelogramoid