Recent progress on harmonic manifolds
Jeong Hyeong Park (Sungkyunkwan University)
Abstract: A Riemannian manifold (M, g) is harmonic if there exists a nonconstant radial harmonic function in a punctured neighborhood for any point, or equivalently if a volume density function centered at a point depends only on the distance from the center. There are many other characterizations of harmonic spaces. For example, it is known that (M, g) is a harmonic space if and only if every sufficiently small geodesic sphere has constant mean curvature. Szabo proved that in a harmonic space, the volume of the intersection of two geodesic balls of small radii depends only on the radii and the distance between the centers. In this talk, we classify harmonic spaces by using the asymptotic series of the density function and eigenvalues of the Jacobi operator, and characterize harmonic spaces in terms of the radial eigenspaces of the Laplacian. We discuss our recent progress on harmonic spaces. (This is joint work with P. Gilkey)
differential geometry
Audience: researchers in the topic
( video )
Virtual seminar on geometry with symmetries
Series comments: Description: Research seminar in Lie group actions in Riemannian geometry.
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Organizers: | Fernando Galaz-GarcĂa*, Carolyn Gordon, Ramiro Lafuente*, Emilio Lauret* |
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