Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userThe analytic torsion of a cone over a sphere
101
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We compute the analytic torsion of a cone over a sphere of dimension 1, 2, and 3, and we conjecture a general formula for the cone over an odd dimensional sphere.
rate research
Read More
We give an explicit formula for the $L^2$ analytic torsion of the finite metric cone over an oriented compact connected Riemannian manifold. We provide an interpretation of the different factors appearing in this formula. We prove that the analytic torsion of the cone is the finite part of the limit obtained collapsing one of the boundaries, of the ratio of the analytic torsion of the frustum to a regularising factor. We show that the regularising factor comes from the set of the non square integrable eigenfunctions of the Laplace Beltrami operator on the cone.
The purpose of this article is to study the asymptotic expansion of Ray-Singer analytic tosion associated with increasing powers p of a given positive line bundle. Here we prove that the asymptotic expansion associated to a manifold contains only the terms of the form $p^{n-i} log p, p^{n-i}$ for $i$-natural. For the two leading terms it was proved by Bismut and Vasserot in 1989. We will calculate the coefficients of the terms $p^{n-1} log p, p^{n-1}$ in the Kahler case and thus answer the question posed in the recent work of Klevtsov, Ma, Marinescu and Wiegmann about quantuum Hall effect. Our second result concerns the general asymptotic expansion of Ray-Singer analytic torsion for an orbifold.
In this paper, we consider a natural map from the Kahler cone to the balanced cone of a Kahler manifold. We study its injectivity and surjecticity. We also give an analytic characterization theorem on a nef class being Kahler.
We study a fractional conformal curvature flow on the standard unit sphere and prove a perturbation result of the fractional Nirenberg problem with fractional exponent $sigma in (1/2,1)$. This extends the result of Chen-Xu (Invent. Math. 187, no. 2, 395-506, 2012) for the scalar curvature flow on the standard unit sphere.
We introduce and study a notion of `Sasaki with torsion structure (ST) as an odd-dimensional analogue of Kahler with torsion geometry (KT). These are normal almost contact metric manifolds that admit a unique compatible connection with 3-form torsion. Any odd-dimensional compact Lie group is shown to admit such a structure; in this case the structure is left-invariant and has closed torsion form. We illustrate the relation between ST structures and other generalizations of Sasaki geometry, and explain how some standard constructions in Sasaki geometry can be adapted to this setting. In particular, we relate the ST structure to a KT structure on the space of leaves, and show that both the cylinder and the cone over an ST manifold are KT, although only the cylinder behaves well with respect to closedness of the torsion form. Finally, we introduce a notion of `G-moment map. We provide criteria based on equivariant cohomology ensuring the existence of these maps, and then apply them as a tool for reducing ST structures.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
