Mathematics – Differential Geometry
Scientific paper
2009-12-11
Mathematics
Differential Geometry
14 pages
Scientific paper
Let $\pi:(E,\nabla^{E}) \to (M,g)$ be an affine submersion with horizontal distribution, where $\nabla^{E}$ is a symmetric connection and $M$ is a Riemannian manifold. Let $\sigma$ be a section of $\pi$, namely, $\pi \circ \sigma = Id_{M}$. It is possible to study the harmonic property of section $\sigma$ in two ways. First, we see $\sigma$ as a harmonic map. Second, we see $\sigma$ as harmonic section. In the Riemannian context, it means that $\sigma$ is a critical point of the vertical functional energy. Our main goal is to find conditions to the assertion: $\sigma$ is a harmonic map if and only if $\sigma$ is a harmonic section.
No associations
LandOfFree
An equivalence between harmonic sections and sections that are harmonic maps does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with An equivalence between harmonic sections and sections that are harmonic maps, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An equivalence between harmonic sections and sections that are harmonic maps will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-468290