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In Vivo Brillouin Analysis of Lens Nucleus and Cortex in Adult Myopic Eyes and Their Correlation With Accommodation. [PDF]

Invest Ophthalmol Vis Sci
Chang L, Song F, Qu S, Cao H, Wu Y, Xu L, Wang J, Zhang R, Xue C, Wang Y.   +9 more
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Pluriclosed Manifolds with Constant Holomorphic Sectional Curvature

Acta Mathematica Sinica. English series, 2021
A long-standing conjecture in complex geometry says that a compact Hermitian manifold with constant holomorphic sectional curvature must be Kähler when the constant is non-zero and must be Chern flat when the constant is zero.
Pei Pei Rao, Fangting Zheng
semanticscholar   +1 more source

On the moduli spaces of metrics with nonnegative sectional curvature

Annals of Global Analysis and Geometry, 2017
The Kreck–Stolz $$s$$ s invariant is used to distinguish connected components of the moduli space of positive scalar curvature metrics. We use a formula of Kreck and Stolz to calculate the $$s$$ s invariant for metrics on $$S^n$$ S n bundles with ...
McFeely Jackson Goodman
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The Weighted Connection and Sectional Curvature for Manifolds With Density

Journal of Geometric Analysis, 2017
In this paper we study sectional curvature bounds for Riemannian manifolds with density from the perspective of a weighted torsion-free connection introduced recently by the last two authors.
Lee Kennard, W. Wylie, Dmytro Yeroshkin
semanticscholar   +1 more source

The geometry of sectional curvatures

General Relativity and Gravitation, 1976
A large class of questions in differential geometry involves the relationship between the geometry and the topology of a Riemannian (= positive-definite) manifold. We briefly review the status of the following question from this class: given that a compact, even-dimensional manifold admits a Riemannian metric of positive sectional curvatures, what can ...
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Sectional Curvature Comparison II

1998
In the previous chapter we classified complete spaces with constant curvature. The goal of this chapter is to compare manifolds with variable curvature to spaces with constant curvature. Our first global result is the Hadamard-Cartan theorem, which says that a simply connected complete manifold with \(\sec \leq 0\) is diffeomorphic to \(\mathbb{R}^{n}\)
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Sectional Curvature-Type Conditions on Metric Spaces

, 2016
In the first part Busemann concavity as non-negative curvature is introduced and a bi-Lipschitz splitting theorem is shown. Furthermore, if the Hausdorff measure of a Busemann concave space is non-trivial then the space is doubling and satisfies a ...
Martin Kell
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Sectional curvatures in nonlinear optimization [PDF]

Journal of Global Optimization, 2007
The aim of the paper is to show how to explicitly express the function of sectional curvature with the first and second derivatives of the problem's functions in the case of submanifolds determined by equality constraints in the n-dimensional Euclidean space endowed with the induced Riemannian metric, which is followed by the formulation of the ...
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Association between cervical lordotic curvature and cervical muscle cross‐sectional area in patients with loss of cervical lordosis

Clinical anatomy (New York, N.Y. Print), 2018
Disruption of the cervical lordotic curve can cause undesirable symptoms such as neck pain, and cord compression. The purpose of this study was to investigate the biomechanics of loss of cervical lordosis by measuring the cross‐sectional area (CSA) of ...
Seo Yeon Yoon, H. Moon, Sang Chul Lee, N. L. Eun, Yong Wook Kim   +4 more
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Sectional curvature and tidal accelerations

Journal of Mathematical Physics, 1990
Sectional curvature is related to tidal accelerations for small objects of nonzero rest mass. Generically, the magnification of tidal accelerations due to high speed goes as the square of the magnification of energy. However, some space-times have directions with bounded increases in tidal accelerations for relativistic speeds.
John K. Beem, Phillip E. Parker
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