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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Metric geometric aspects of Einstein manifolds
Einstein流形 度量几何 爱因斯坦流形 黎曼几何
2023/11/29
This lecture concerns the metric Riemannian geometry of Einstein manifolds, which is a central theme in modern differential geometry and is deeply connected to a large variety of fundamental problems ...
Optimal Riemannian metric for a volumorphism and a mean ergodic theorem in complete global Alexandrov nonpositively curved spaces
Optimal Riemannian metric volumorphism mean ergodic theorem complete global Alexandrov nonpositively curved spaces Differential Geometry
2012/6/15
In this paper we give a natural condition for when a volumorphism on a Riemannian manifold $(M,g)$ is actually an isometry with respect to some other, optimal, Riemannian metric $h$. We consider the n...
A Tale of Two Arc Lengths: Metric notions for curves in surfaces in equiaffine space
anne curve anne arc length anne surface anne first fundamental form
2012/5/9
In Euclidean geometry, all metric notions (arc length for curves, the first fundamental form for surfaces, etc.) are derived from the Euclidean inner product on tangent vectors, and this inner product...
Adapted connections on metric contact manifolds
Adapted connections metric contact manifolds Differential Geometry
2012/4/16
In this paper, we describe the space of adapted connections on a metric contact manifold through the space of their torsion tensors. The torsion tensor is an element of the space of TM-valued two-form...
Local convexity properties of Apollonian and Seittenranta's metric balls
Apollonian distance Seittenranta’s distance metric ball local convexity
2012/4/17
We consider local convexity properties of the Apollonian and the Seittenranta's metric balls. The Apollonian metric balls are considered in the twice punctured space, convex and starlike domains. The ...
Improved geodesics for the reduced curvature-dimension condition in branching metric spaces
Ricci curvature metric measure spaces branching metric spaces Differential Geometry
2012/3/1
In this note we show that in metric measure spaces satisfying the reduced curvature-dimension condition CD*(K,N) we always have geodesics in the Wasserstein space of probability measures that satisfy ...
Para-CR Structures on almost Paracontact Metric Manifolds
Para-CR manifolds para-Sasakian manifolds almost paracontact metric manifolds paracontact metric manifolds
2012/3/1
Almost paracontact metric manifolds are the famous examples of almost para-CR manifolds. We find necessary and suffcient conditions for such manifolds for be para-CR. Next we examine these conditions ...
Abstract: Cheeger's finiteness theorem bounds the number of diffeomorphism types of manifolds with bounded curvature, diameter and volume; the Hadamard--Cartan theorem, as popularized by Gromov, shows...
The Intrinsic Geometry of Almost Contact Metric Manifolds
almost contact manifold Sasakian manifold K-contact manifold the intrinsic geometry of almost contact metric manifolds
2011/9/22
Abstract: In this paper the notion of the intrinsic geometry of an almost contact metric manifold is introduced. Description of some classes of spaces with almost contact metric structures in terms of...
Local Poincare inequalities from stable curvature conditions on metric spaces
Ricci curvature metric measure spaces geodesics Poincare inequality
2011/9/20
Abstract: We prove local Poincar\'e inequalities under various curvature-dimension conditions which are stable under the measured Gromov-Hausdorff convergence. The first class of spaces we consider is...
Abstract: This is a pedagogical introduction covering maps of metric spaces, Gromov-Hausdorff distance and its "physical" meaning, and dilation structures as a convenient simplification of an exhausti...
Classical integral geometry takes place in Rn equipped with the Euclidean metric. We begin to develop integral geometry for Rn equipped with the taxicab metric (induced by the 1-norm).
This is a survey on nondiscrete euclidean buildings, with a focus on metric properties of these spaces.
Quantum Geometric Tensor (Fubini-Study Metric) in Simple Quantum System: A pedagogical Introduction
Quantum Geometric Tensor Simple Quantum System pedagogical Introduction
2011/3/2
Geometric Quantum Mechanics is a novel and prospecting approach motivated by the belief that
our world is ultimately geometrical. At the heart of that is a quantity called Quantum Geometric Tensor (o...
Mixed Non-Expansive and Potentially Expansive Properties of a Class of Self-Maps in Metric Spaces
contractive maps non-expansive maps metric space fixed points
2010/12/15
This paper investigates self-maps T : X X which satisfy a distance constraint in a metric
space which mixed point-dependent non-expansive properties, or in particular contractive ones, and p...