Residue-torsion and the Laplacian on Riemannian manifolds
نویسندگان
چکیده
The Ray–Singer analytic torsion is the classical zeta-trace of a sum logarithm operators p-form Laplacians on de Rham complex. In this article, we examine residue-analytic torsion, defined using residue trace in place zeta function regularised trace.
منابع مشابه
A Geometry Preserving Kernel over Riemannian Manifolds
Abstract- Kernel trick and projection to tangent spaces are two choices for linearizing the data points lying on Riemannian manifolds. These approaches are used to provide the prerequisites for applying standard machine learning methods on Riemannian manifolds. Classical kernels implicitly project data to high dimensional feature space without considering the intrinsic geometry of data points. ...
متن کاملFlowers on Riemannian manifolds
In this paper we will present two upper bounds for the length of a smallest “flower-shaped” geodesic net in terms of the volume and the diameter of a manifold. Minimal geodesic nets are critical points of the length functional on the space of graphs immersed into a Riemannian manifold. Let Mn be a closed Riemannian manifold of dimension n. We prove that there exists a minimal geodesic net that ...
متن کاملA Global Curvature Pinching Result of the First Eigenvalue of the Laplacian on Riemannian Manifolds
and Applied Analysis 3 then there exists a constant C 3 (n) > 0 such that λ 1 (M) ≥ C 3 (n). Proof. The proof mainly belongs to Li and Yau [6]. Let u be the normalized eigenfunction ofM, set V = log (a + u) where a > 1. Then, we can easily get that ΔV = −λ 1 (M) u a + u − |∇V| 2 . (8) Denote that Q(x) = |∇V|(x), and we then have by the Ricci identity on manifolds with Ric (M) ≥ 0:
متن کاملOn non-Riemannian Superconductors and torsion loops
The geometrization of electrodynamics is obtained by performing the complex extension of the covariant derivative operator to include the Cartan torsion vector and applying this derivative to the Ginzburg-Landau equation of superfluids and Superconductors.It is shown that the introduction of torsion makes a shift in the symmetry breaking vacuum.Torsion loops are computed from geometrical phases...
متن کاملMetallic Structures on Riemannian Manifolds
Our aim in this paper is to focus on some applications in differential geometry of the metallic means family (a generalization of the golden mean) and generalized Fibonacci sequences, using a class of polynomial structures defined on Riemannian manifolds. We search for properties of the induced structure on a submanifold by metallic Riemannian structures and we find a necessary and sufficient c...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications in Partial Differential Equations
سال: 2021
ISSN: ['1532-4133', '0360-5302']
DOI: https://doi.org/10.1080/03605302.2020.1871365