Rigidity of lattices of non-positive curvature

Rigidity in Non-negative Curvature

In this paper we will show that any complete manifold of nonnegative curvature has a flat soul provided it has curvature going to zero at infinity. We also show some similar results about manifolds with bounded curvature at infinity. To establish these theorems we will prove some rigidity results for Riemannian submersions, eg., any Riemannian submersion with complete flat total space and compa...

The Radius Rigidity Theorem for Manifolds of Positive Curvature

Recall that the radius of a compact metric space (X, dist) is given by rad X = minx∈X maxy∈X dist(x, y). In this paper we generalize Berger’s 1 4 -pinched rigidity theorem and show that a closed, simply connected, Riemannian manifold with sectional curvature ≥ 1 and radius ≥ π2 is either homeomorphic to the sphere or isometric to a compact rank one symmetric space. The classical sphere theorem ...

of non-positive Gaussian curvature

Quasi-isometric rigidity of non-cocompact S-arithmetic lattices

Throughout we let K be an algebraic number field, VK the set of all inequivalent valuations on K, and V ∞ K ⊆ VK the subset of archimedean valuations. We will use S to denote a finite subset of VK that contains V ∞ K , and we write the corresponding ring of S-integers in K as OS. In this paper, G will always be a connected non-commutative absolutely simple algebraic K-group. Any group of the fo...

investigation of effective parameters on the rigidity of light composite diaphragms (psscb) by fem

در این رساله با معرفی سقف های psscb متشکل از ترکیب ورق های فولادی ذوزنقه ای و تخته های سیمانی الیافی به عنوان سقف های پیش ساخته (سازگار با سیستم سازه ای قاب های فولادی سبک) به بررسی پارامترهای موثر بر صلبیت سقف، پرداخته می شود. در تحقیق حاضر ابتدا به مدل سازی دو نمونه سقف آزمایش شده، به روش اجزاء محدود با استفاده از نرم افزار تحلیلی abaqus ver 6.10 پرداخته شده است. نمونه های ساخته شده تحت اعما...