Does anyone know of an explicit calculation of a Levi-Civita connection? It is a map from $V\times V \rightarrow V$ where $V$ is the set of all vector fields on a manifold $M$, so there should be an explicit way of writing such a map for a particular LC connection but I can't find any.
2026-03-29 03:22:28.1774754548
Levi-Civita Connection Example of a calculation
518 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in DIFFERENTIAL-GEOMETRY
- Smooth Principal Bundle from continuous transition functions?
- Compute Thom and Euler class
- Holonomy bundle is a covering space
- Alternative definition for characteristic foliation of a surface
- Studying regular space curves when restricted to two differentiable functions
- What kind of curvature does a cylinder have?
- A new type of curvature multivector for surfaces?
- Regular surfaces with boundary and $C^1$ domains
- Show that two isometries induce the same linear mapping
- geodesic of infinite length without self-intersections
Related Questions in RIEMANNIAN-GEOMETRY
- What is the correct formula for the Ricci curvature of a warped manifold?
- How to show that extension of linear connection commutes with contraction.
- geodesic of infinite length without self-intersections
- Levi-Civita-connection of an embedded submanifold is induced by the orthogonal projection of the Levi-Civita-connection of the original manifold
- Geodesically convex neighborhoods
- The induced Riemannian metric is not smooth on the diagonal
- Intrinsic vs. Extrinsic notions of Harmonic maps.
- Equivalence of different "balls" in Riemannian manifold.
- Why is the index of a harmonic map finite?
- A closed manifold of negative Ricci curvature has no conformal vector fields
Related Questions in SMOOTH-MANIFOLDS
- Smooth Principal Bundle from continuous transition functions?
- Possible condition on locally Euclidean subsets of Euclidean space to be embedded submanifold
- "Defining a smooth structure on a topological manifold with boundary"
- Hyperboloid is a manifold
- The graph of a smooth map is a manifold
- A finite group G acts freely on a simply connected manifold M
- An elementary proof that low rank maps cannot be open
- What does it mean by standard coordinates on $R^n$
- Partial Differential Equation using theory of manifolds
- Showing that a diffeomorphism preserves the boundary
Related Questions in CONNECTIONS
- Holonomy bundle is a covering space
- How to show that extension of linear connection commutes with contraction.
- Levi-Civita-connection of an embedded submanifold is induced by the orthogonal projection of the Levi-Civita-connection of the original manifold
- Conectionless parallel transport
- Holonomy group and irreducible $\mathrm{SU}(2)$-connections
- How is the covariant derivative of a metric, $\nabla g$, defined?
- Different definitions of irreducible $\mathrm{SU}(2)$ connections
- If $\nabla X=h \cdot \text{Id}_{TM}$ for a vector field $X$ and $h \in C^{\infty}(M)$, is $h$ constant?
- Connection on a vector bundle in terms of sections
- Passage in the proof of Chern-Weil method in John Roe's Elliptic operators book
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?