We construct a metrical framed structure on the tensor bundle of a Riemannian manifold equipped with a Cheeger-Gromoll type metric and by restricting this structure to the tensor sphere bundle, we obtain an almost metrical paracontact structure on the tensor sphere bundle. Moreover, we show that the tensor sphere bundles endowed with the induced metric are never space forms.
Natural metrics (Sasaki metric, Cheeger-Gromoll metric, Kaluza-Klein metrics etc.. ) on the tangent bundle of a Riemannian manifold is a central topic in Riemannian geometry. Generalized Cheeger-Gromoll metrics is a family of natural metrics $h_{p,q}$ depending on two parameters with $p\in\mathbb{R}$ and $q\geq0$. This family has been introduced recently and possesses interesting geometric properties. If $p=q=0$ we recover the Sasaki metric and when $p=q=1$ we recover the classical Cheeger-Gromoll metric. A transitive Euclidean Lie algebroid is a transitive Lie algebroid with an Euclidean prod…
The purpose of this paper is two-fold: we systematically introduce the notion of Cheeger deformations on fiber bundles with compact structure groups, and recover in a very simple and unified fashion several results that either already appear in the literature or are known by experts, though are not explicitly written elsewhere. We re-prove: Schwachhöfer--Tuschmann Theorem on bi-quotients, many results due to Fukaya and Yamaguchi, as well as, naturally extend the work of Searle--Solórzano--Wilhelm on regularization properties of Cheeger deformations, among others. In this sense, this paper shou…
We generalize a Cheeger-Müller type theorem for flat, unitary bundles on infinite covering spaces over manifolds-with-boundary, proven by Burghelea, Friedlander and Kappeller arXiv:dg-ga/9510010 [math.DG]. Employing recent anomaly results by Brüning, Ma and Zhang, we prove an analogous statement for a general flat bundle that is only required to have a unimodular restriction to the boundary.
We prove that a compact $RCD^*(0,N)$ (or equivalently $RCD(0,N)$) metric measure space, $\left(X, d, m \right)$, with $\diam X \le d$ and its first (nonzero) eigenvalue of the Laplacian (in the sense of Ambrosio-Gigli-Savaré) , $λ_1 = \frac{π^2}{d^2}$, has to be a circle or a line segment with diameter, $π$. This completely characterizes the equality in Zhong-Yang type sharp spectral gap estimates in the metric measure setting with Riemannian lower Ricci bounds. Among such spaces, are the familiar Riemannian manifolds with $\Ric \ge 0$, $(0,N)-$ Bakry-Émery manifolds, $(0,n)-$ Ricci limit spac…
A Geometric Realization of Spherical T-Duality via $\star$-Diagrams
Institute of Mathematics and Informatics（数学与信息学研究所）；IMECC, Universidade Estadual de Campinas（坎皮纳斯州立大学计算、工程和数学学院）；Department of Mathematics, University of Miami（迈阿密大学数学系）；Institute of the Mathematical Sciences of the Americas（美洲数学科学研究所）；International Center for Mathematical Sciences（国际数学科学中心）
