User contributions for Vipul
24 July 2009
- 21:5321:53, 24 July 2009 diff hist +1,634 N Tensor product of flat connections is flat Created page with '==Statement== Suppose <math>M</math> is a differential manifold and <math>E,E'</math> are vector bundles over <math>M</math>. Suppose <math>\nabla, \nabla'</math> are [[…'
- 21:4721:47, 24 July 2009 diff hist +1 Tensor product of connections →Facts current
- 21:4621:46, 24 July 2009 diff hist +886 Tensor product of connections No edit summary
- 21:3921:39, 24 July 2009 diff hist +856 N Formula for curvature of tensor product of connections Created page with '==Statement== Suppose <math>E,E'</math> are vector bundles over a differential manifold <math>M</math>. Suppose <math>\nabla,\nabla'</math> are connections on <math>…' current
- 21:3021:30, 24 July 2009 diff hist −65 Tensor product of metric connections is metric No edit summary
- 21:2921:29, 24 July 2009 diff hist +701 N Tensor product of metric connections is metric Created page with '==Statement== A differential manifold <math>M</math>. Two fact about::metric bundles <math>(E,g)</math> and <math>(E',g')</math> (i.e., <math>E,E'</math> are [[vector bu…'
- 21:2521:25, 24 July 2009 diff hist +1 Tensor product of connections No edit summary
- 21:2421:24, 24 July 2009 diff hist +1,181 Direct sum of connections No edit summary current
- 21:2321:23, 24 July 2009 diff hist +139 Tensor product of connections →Distributivity with direct sum
- 21:2121:21, 24 July 2009 diff hist +473 N Direct sum of connections Created page with '==Definition== Suppose <math>M</math> is a differential manifold and <math>E,E'</math> are vector bundles on <math>M</math>. Suppose <math>\nabla,\nabla'</math> are [[de…'
- 21:1821:18, 24 July 2009 diff hist +452 Connection on a vector bundle →Constructions
- 21:1521:15, 24 July 2009 diff hist +2,812 N Tensor product of connections Created page with '==Definition== Suppose <math>E,E'</math> are vector bundles over a differential manifold <math>M</math>. Suppose <math>\nabla</math> is a [[fact about::connection on a v…'
- 21:0221:02, 24 July 2009 diff hist +259 Levi-Civita connection No edit summary
- 20:5420:54, 24 July 2009 diff hist −184 Levi-Civita connection →Facts
- 20:5420:54, 24 July 2009 diff hist +17 Levi-Civita connection →Christoffel symbols
- 19:5319:53, 24 July 2009 diff hist +460 Levi-Civita connection No edit summary
- 18:4318:43, 24 July 2009 diff hist +4,645 N Levi-Civita connection exists and is unique Created page with '==Statement== Suppose <math>M</math> is a differential manifold and <math>g</math> is a fact about::Riemannian metric or a fact about::pseudo-Riemannian metric. Then…' current
- 18:4218:42, 24 July 2009 diff hist +6 Corollary of Leibniz rule for Lie bracket No edit summary current
- 16:1316:13, 24 July 2009 diff hist −947 Levi-Civita connection No edit summary
- 02:2902:29, 24 July 2009 diff hist +57 Ricci curvature tensor No edit summary current
- 02:2802:28, 24 July 2009 diff hist +45 Ricci curvature tensor of Levi-Civita connection →Definition current
- 02:2702:27, 24 July 2009 diff hist +86 Ricci curvature tensor of Levi-Civita connection No edit summary
- 02:2602:26, 24 July 2009 diff hist +63 Scalar curvature No edit summary current
- 02:2402:24, 24 July 2009 diff hist +2 Curvature is symmetric in the pairs of first and last two variables →Proof current
- 02:2402:24, 24 July 2009 diff hist +16 Curvature is symmetric in the pairs of first and last two variables No edit summary
- 02:2302:23, 24 July 2009 diff hist +2,136 N Curvature is symmetric in the pairs of first and last two variables Created page with '==Statement== Suppose <math>M</math> is a differential manifold and <math>g</math> is a fact about::Riemannian metric or fact about::pseudo-Riemannian metric on <mat…'
- 01:5401:54, 24 July 2009 diff hist +129 Curvature is tensorial →Related facts
- 01:5201:52, 24 July 2009 diff hist +178 Curvature is antisymmetric in last two variables No edit summary current
- 01:5101:51, 24 July 2009 diff hist +1 Curvature is antisymmetric in last two variables →Proof
- 01:5001:50, 24 July 2009 diff hist −4 Curvature is antisymmetric in last two variables →Proof
- 01:5001:50, 24 July 2009 diff hist +1,415 Curvature is antisymmetric in last two variables No edit summary
- 01:2801:28, 24 July 2009 diff hist +879 N Curvature is antisymmetric in last two variables Created page with '==Statement== Suppose <math>M</math> is a differential manifold and <math>g</math> is a fact about::Riemannian metric or fact about::pseudo-Riemannian metric and <ma…'
- 01:2301:23, 24 July 2009 diff hist +24 Second Bianchi identity No edit summary current
- 01:2201:22, 24 July 2009 diff hist +120 Riemann curvature tensor of Levi-Civita connection No edit summary current
- 01:1901:19, 24 July 2009 diff hist +36 Torsion is tensorial No edit summary
- 01:1801:18, 24 July 2009 diff hist +3 Torsion is tensorial →Proof
- 01:1801:18, 24 July 2009 diff hist +12 Torsion is tensorial →Facts used
- 01:1701:17, 24 July 2009 diff hist +246 Curvature is antisymmetric in first two variables No edit summary current
- 01:1401:14, 24 July 2009 diff hist +158 First Bianchi identity No edit summary current
- 01:1301:13, 24 July 2009 diff hist +36 First Bianchi identity No edit summary
- 01:1101:11, 24 July 2009 diff hist +22 Curvature is tensorial No edit summary
- 01:1101:11, 24 July 2009 diff hist +76 Curvature is tensorial No edit summary
- 01:1001:10, 24 July 2009 diff hist +18 Curvature is tensorial →Proof
- 00:4200:42, 24 July 2009 diff hist +927 Connection is module structure over connection algebra →From a connection to a module structure current
- 00:2600:26, 24 July 2009 diff hist +282 Connection is module structure over connection algebra →From a connection to a module structure
- 00:1900:19, 24 July 2009 diff hist +28 Connection is module structure over connection algebra →From a connection to a module structure
- 00:1800:18, 24 July 2009 diff hist +665 Connection is module structure over connection algebra No edit summary
23 July 2009
27 March 2009
- 11:2911:29, 27 March 2009 diff hist −24 Template:Top notice No edit summary
- 11:2211:22, 27 March 2009 diff hist −687 Main Page Replaced content with '{{top notice}}' current