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New post in Connections
Calculate time to fill an empty tank
December 18th, 2020
connections
Calculating Levi-Civita Connection and Curvature for Euclidean Metric
May 2nd, 2020
differential-geometry
metric-spaces
manifolds
curvature
connections
Is the autoparallel equation same as the geodesic equation?
April 2nd, 2020
connections
geodesic
definition
differential-geometry
Prove that the curvature of a connection on a line bundle is a global two form
August 1st, 2022
differential-geometry
connections
vector-bundles
geometry
Parallel transport around a closed loop
May 21st, 2020
riemannian-geometry
curvature
tensors
differential-geometry
connections
Covariant derivative of tensor densities
May 6th, 2020
tensors
connections
differential-geometry
Deriving Ricci identity for co-vector fields
March 12th, 2020
tensors
differential-geometry
riemannian-geometry
connections
Lie derivative characterisation of the Levi-Civita connection
May 26th, 2020
differential-geometry
lie-derivative
connections
riemannian-geometry
Definition of formal adjoint of covariant derivative
June 29th, 2020
differential-geometry
connections
differential-operators
How are the definitions of Christoffel symbols from the metric and from $\nabla_i\partial_j$ related?
September 28th, 2021
connections
differential-geometry
Divergence as trace of Levi-Civita connection
August 1st, 2022
differential-geometry
connections
Difference of two connections is a tensor
August 1st, 2022
differential-geometry
tensors
vector-bundles
connections
manifolds
What does it mean intuitively for a metric and connection to be compatible?
February 27th, 2020
general-relativity
differential-geometry
riemannian-geometry
intuition
connections
How is the covariant derivative of a metric, $\nabla g$, defined?
July 11th, 2021
riemannian-geometry
connections
differential-geometry
Tangential component of a Riemannian connection
August 1st, 2022
differential-geometry
riemannian-geometry
connections
submanifold
Prove that the Christoffel symbols vanish in $\mathbb{R}^n$
September 28th, 2021
differential-geometry
riemannian-geometry
connections
Equivalence for Christoffel symbol and Koszul formula
August 1st, 2022
connections
riemannian-geometry
How to define a covariant derivative on a smooth vector bundle using only an Ehresmann connection?
August 1st, 2022
connections
differential-geometry
definition
smooth-manifolds
vector-bundles
Proving that Levi-Civita connection is preserved by isometries
August 1st, 2022
differential-geometry
riemannian-geometry
connections
manifolds
Levi-Civita-connection of an embedded submanifold is induced by the orthogonal projection of the Levi-Civita-connection of the original manifold
January 16th, 2020
riemannian-geometry
manifolds
differential-geometry
connections
How to define a connection on the dual bundle?
August 1st, 2022
connections
vector-bundles
differential-geometry
Flat bundle and constant transition functions
September 26th, 2020
differential-geometry
connections
vector-bundles
Curvature of pullback connection
September 13th, 2021
differential-geometry
connections
curvature
vector-bundles
riemannian-geometry
Affine connection on a Lie group.
August 1st, 2020
differential-topology
connections
lie-algebras
lie-groups
differential-geometry
$X$ is a Killing field $\iff \langle \nabla_YX,Z \rangle+\langle \nabla _ZX,Y\rangle=0$
August 1st, 2022
connections
vector-fields
riemannian-geometry
Proving the Ricci identity
August 1st, 2022
riemannian-geometry
connections
tensors
general-relativity
differential-geometry
Covariant derivative of a vector field along a curve
August 1st, 2022
differential-geometry
connections
Why is the space of all connection on a vector bundle an affine space?
August 1st, 2022
connections
vector-bundles
differential-geometry
Most succinct proof of the uniqueness and existence of the Levi-Civita connection.
August 1st, 2022
connections
riemannian-geometry
differential-geometry
Covariant derivative versus exterior derivative
August 1st, 2022
connections
differential-geometry
differential-forms
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