Statements (99)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:academic
gptkb:mathematical_concept |
| gptkbp:appliesTo |
gptkb:general_relativity
computer science engineering physics robotics |
| https://www.w3.org/2000/01/rdf-schema#label |
Differential Geometry
|
| gptkbp:notableIdea |
gptkb:Bott_periodicity
gptkb:Stokes'_theorem gptkb:geometry gptkb:Hodge_theory gptkb:fiber gptkb:Frobenius_theorem gptkb:Metric gptkb:Riemannian_manifold gptkb:Tensor gptkb:Lie_group gptkb:Morse_theory gptkb:Chern_class gptkb:Atiyah-Singer_index_theorem gptkb:Cartan's_moving_frame gptkb:Christoffel_symbols gptkb:Donaldson_theory gptkb:Gauss-Bonnet_theorem gptkb:Gromov-Witten_invariant gptkb:Hopf_fibration gptkb:Laplace-Beltrami_operator gptkb:Seiberg-Witten_theory gptkb:Weingarten_map gptkb:Willmore_energy gptkb:Yamabe_problem gptkb:mean_curvature_flow gptkb:Cartan_connection gptkb:Ricci_flow gptkb:twistor_space gptkb:de_Rham_cohomology differential topology Gaussian curvature Kähler manifold Nash embedding theorem isometry pseudo-Riemannian manifold symplectic manifold immersion differential form differential operator embedding flow vector bundle connection form holonomy Dirac operator Euler class G-structure Levi-Civita connection Pfaffian system Pontryagin class Ricci curvature affine connection connection cotangent space covariant derivative curvature extrinsic curvature first fundamental form foliation frame bundle harmonic map holomorphic vector bundle intrinsic curvature jet bundle mean curvature minimal submanifold minimal surface normal vector parallel transport principal curvature second fundamental form sectional curvature shape operator spin structure submanifold tangent space torsion vector field |
| gptkbp:relatedTo |
gptkb:algebraic_geometry
gptkb:topology gptkb:Riemannian_geometry symplectic geometry complex geometry |
| gptkbp:studies |
differentiable manifolds
geometry of smooth shapes |
| gptkbp:uses |
calculus
partial differential equations linear algebra multilinear algebra |
| gptkbp:bfsParent |
gptkb:James_J._Stoker
|
| gptkbp:bfsLayer |
5
|