Intereting Posts

Prove Transformation is one-to-one iff it carries linearly independent subsets of $V$ onto Lin. Ind. subsets of $W$.
Classic Circle and Adjacent Arrangement Problem
Closed form for $ S(m) = \sum_{n=1}^\infty \frac{2^n \cdot n^m}{\binom{2n}n} $ for integer $m$?
Proof that $\sqrt x$ is absolutely continuous.
If a finite group $G$ is solvable, is $$ nilpotent?
How can I show that the set of rational numbers with denominator a power of two form a dense subset of the reals?
Critiques on proof showing $\sqrt{12}$ is irrational.
Counting number of solutions with restrictions
Affine transformation
Deep theorem with trivial proof
Proof of $a^n+b^n$ divisible by a+b when n is odd
Plotting a Function of a Complex Variable
why symmetric matrices are diagonalizable?
About the equivalence of definitions of a Baire Space
The graph of the function $f(x)= \left\{ \frac{1}{2 x} \right\}- \frac{1}{2}\left\{ \frac{1}{x} \right\} $ for $0<x<1$

Let $A$ and $B$ be two surfaces (smooth enough) in an affine space $M$ with metric $g$. Let $g^A$, $g^B$ be the metric tensors on the two surfaces induced by $g$, and $\nabla^A$, $\nabla^B$ the Levi-Civita connections on the two surfaces. Let $f:A\rightarrow B$ be a diffeomorphism.

I’m wondering if, given a vector field $X^B$ on $B$, there is an expression for $f^* (\nabla^{B} X^B)$. I think it should be something including $\nabla^A(f^*X^B)$, but I can’t find it.

Thanks for your help.

- Why isn't the 3 body problem solvable?
- How to Show Cotangent Bundles Are Not Compact Manifolds?
- Stress vector - Stress tensor
- Euler-Lagrange equations of the Lagrangian related to Maxwell's equations
- What if the Euler Lagrange equation yields a 'trivial' answer
- Does the Cauchy-Lipschitz theorem extend to higher order DEs?

- What is the affine connection, and what is the intuition behind/for affine connection?
- Equivalence for Christoffel symbol and Koszul formula
- Equivalent conditions for a linear connection $\nabla$ to be compatible with Riemannian metric $g$
- How to introduce stress tensor on manifolds?
- Frictional forces
- How to calculate the velocity for this
- Euler-Lagrange equations of the Lagrangian related to Maxwell's equations
- Does the Cauchy-Lipschitz theorem extend to higher order DEs?
- Covariant derivative versus exterior derivative
- What if the Euler Lagrange equation yields a 'trivial' answer

- $\binom{n}{1},\binom{n}{2},\ldots ,\binom{n}{n-1}$ are all even numbers.
- Are there mathematical objects that have been proved to exist but cannot be described in words?
- $n$ times integrated Brownian motion
- Defining the Product of Ideals
- Large variance implies small probability of being in interval
- Homotopy groups of $S^2$
- Wave Operators: Calculus
- Can a Pratt certificate for a prime be found in polynomial time?
- Polynomial uniqueness proof
- Change of freebound variables in Integration
- Inverse image of a compact set is compact
- Hint on a limit that involves the Hurwitz Zeta function
- Assume $f$ is a continuous one-to-one function over an interval. Prove that $f$ is strictly monotone
- Proving a subset is a subspace of a Vector Space
- Prove that T is a linear transformation