Search results

Page title matches

• Category:Facts about regular values
  This category lists important facts about regular values, critical values, regular points and critical points of smooth maps between differential ... ...
  3 members (0 subcategories, 0 files) - 20:16, 18 May 2008

Page text matches

• Isotopy of immersions
  ==Facts== * Immersions in Euclidean space are isotopic in its square ... ...
  683 bytes (130 words) - 19:47, 18 May 2008
• Riemannian density
  ==Facts== ===Invariance=== The Riemannian density is invariant under the Levi-Civita connection. ... ...
  288 bytes (34 words) - 20:07, 18 May 2008
• Gauss-Kronecker curvature of a hypersurface
  ==Facts== * Gauss-Bonnet theorem for hypersurfaces ... ...
  647 bytes (102 words) - 19:41, 18 May 2008
• Cotangent bundle
  ==Facts== differential 1-form|sheaf of differential 1-forms tangent bundle ... ...
  376 bytes (56 words) - 19:36, 18 May 2008
• Strongly convex set
  ==Facts== Given any point, a metric ball of sufficiently small radius about that point is strongly convex. ... ...
  502 bytes (79 words) - 20:10, 18 May 2008
• Jacobi field
  ==Facts== Jacobi fields are precisely the null space of the positive semidefinite quadratic form E_{**} which is defined as: E_{**} (W_1,W_2) ... ...
  745 bytes (120 words) - 19:47, 18 May 2008
• Calabi-Yau manifold
  ==Facts== ===Ricci-flatness=== Yau's theorem tells us that every Calabi-Yau manifold admits a Ricci-flat metric, viz a compatible metric ... ...
  458 bytes (65 words) - 19:33, 18 May 2008
• Null subset of a differential manifold
  ==Facts== * Any submanifold of codimension at least 1, is a measure zero subset * Sard's theorem is a generalization of the above ... ...
  945 bytes (152 words) - 19:50, 18 May 2008
• Restricted holonomy group
  ==Facts== The restricted holonomy group is a normal subgroup of the holonomy group, which comprises all the linear transformations that occur ... ...
  650 bytes (104 words) - 19:51, 18 May 2008
• Ricci curvature determines Ricci curvature tensor
  ==Facts used== * Ricci curvature tensor is symmetric * Symmetric bilinear form is determined by values on same-vector pairs ==Proof== ... ...
  376 bytes (49 words) - 12:54, 22 May 2008
• Derivation
  ==Facts== Every vector field on a differential manifold gives rise to a derivation, and this gives a correspondence between vector fields and ... ...
  738 bytes (119 words) - 19:38, 18 May 2008
• Evolute of a curve
  ==Facts== ===For a planar curve=== * The length of the evolute between any two points is the total variation in the radius of curvature between ... ...
  602 bytes (101 words) - 19:39, 18 May 2008
• Geodesic variation
  ==Facts== A vector field along a geodesic is the variation vector field of a geodesic variation if and only if it is a Jacobi field. ... ...
  445 bytes (73 words) - 19:41, 18 May 2008
• Space of metrics on a bundle
  ==Facts== ===Gauge group acts on the space of metrics=== The gauge group of the vector bundle E acts on the space of metrics of E. ... ...
  592 bytes (105 words) - 20:09, 18 May 2008
• Effective action of finite group of diffeomorphisms has free point
  ==Facts used== We use two main facts: # Fixed-point set of finite group of diffeomorphisms ... ...
  1 KB (259 words) - 19:39, 18 May 2008
• Injectivity radius of a manifold
  ==Facts== ===Klingenberg's theorem=== Klingenberg's theorem A useful way of bounding the injectivity radius of a manifold is the so ... ...
  646 bytes (94 words) - 19:47, 18 May 2008
• Connection along a curve
  ==Facts== ===Connection gives connection along a curve=== Given a connection on the whole vector bundle E, we can obtain a connection along the ... ...
  1 KB (248 words) - 19:35, 18 May 2008
• Segre curve
  ==Facts== ===Segre's theorem=== Segre's theorem Any Segre curve has at least four flattenings. ... ...
  444 bytes (62 words) - 20:08, 18 May 2008
• Complete equals geodesically complete
  ==Facts used== * Uses::Hopf-Rinow theorem ==Proof== ===Complete implies geodesically complete=== ... ...
  833 bytes (131 words) - 13:27, 22 May 2008
• Simple closed curve in the plane
  ==Facts== By the Jordan curve theorem, the simple closed curve divides its complement into exactly two components. One of the components is bounded ... ...
  911 bytes (147 words) - 20:09, 18 May 2008