Space curvature

This book is devoted to the rst acquaintance with the dierential geometry Therefore it begins with the theory of curves in threedimensional Euclidean spac E. Then the vectorial analysis in E is stated both in Cartesian and curvilinea coordinates, afterward the theory of surfaces in the space E is considered. The newly fashionable approach starting with the concept of a dierentiabl manifold, to my opinion, is not suitable for the introduction to the subject.
132p tiramisu0908 31102012 31 10 Download

The Ricci ﬂow was introduced by Hamilton in 1982 [H1] in order to prove that a compact threemanifold admitting a Riemannian metric of positive Ricci curvature is a spherical space form. In dimension four Hamilton showed that compact fourmanifolds with positive curvature operators are spherical space forms as well [H2]. More generally, the same conclusion holds for compact fourmanifolds with 2positive curvature operators [Che]. Recall that a curvature operator is called 2positive, if the sum of its two smallest eigenvalues is positive. ...
20p dontetvui 17012013 26 7 Download

John Archibald Wheeler was born on July 9, 1911, in Jacksonville, Florida, and passed away on April 13, 2008, in Hightstown, New Jersey; his influence on gravitational physics and science in general will remain forever. Among his many and important contributions to physics, he was one of the fathers of the renaissance of General Relativity.
0p tom_123 14112012 28 6 Download

This paper is the fourth in a series where we describe the space of all embedded minimal surfaces of ﬁxed genus in a ﬁxed (but arbitrary) closed 3manifold. The key is to understand the structure of an embedded minimal disk in a ball in R3 . This was undertaken in [CM3], [CM4] and the global version of it will be completed here; see the discussion around Figure 12 for the local case and [CM15] for some more details. Our main results are Theorem 0.1 (the lamination theorem) and Theorem 0.2 (the onesided curvature estimate). ...
44p tuanloccuoi 04012013 26 6 Download

We introduce a class of metric spaces which we call “bolic”. They include hyperbolic spaces, simply connected complete manifolds of nonpositive curvature, euclidean buildings, etc. We prove the Novikov conjecture on higher signatures for any discrete group which admits a proper isometric action on a “bolic”, weakly geodesic metric space of bounded geometry. 1. Introduction This work has grown out of an attempt to give a purely KKtheoretic proof of a result of A. Connes and H. Moscovici ([CM], [CGM]) that hyperbolic groups satisfy the Novikov conjecture. ...
43p tuanloccuoi 04012013 18 5 Download

The space of embedded minimal surfaces of ﬁxed genus in a 3manifold II; Multivalued graphs in disks By Tobias H. Colding and William P. Minicozzi II* 0. Introduction This paper is the second in a series where we give a description of the space of all embedded minimal surfaces of ﬁxed genus in a ﬁxed (but arbitrary) closed 3manifold. The key for understanding such surfaces is to understand the local structure in a ball and in particular the structure of an embedded minimal disk in a ball in R3 . We show here that if the curvature of such a disk...
25p tuanloccuoi 04012013 24 5 Download

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Schauder Fixed Point Theorem in Spaces with Global Nonpositive Curvature
8p sting08 18022012 24 4 Download

This book is based on lectures delivered over the years by the author at the Universit´e Pierre et Marie Curie, Paris, at the University of Stuttgart, and at City University of Hong Kong. Its twofold aim is to give thorough introductions to the basic theorems of differential geometry and to elasticity theory in curvilinear coordinates. The treatment is essentially selfcontained and proofs are complete.
215p kimngan_1 06112012 26 1 Download

Next, a few words about our strategy. It is well recognized now that one has to go beyond the EinsteinHilbert action for gravity, both from the experimental viewpoint (eg.,because of Dark Energy) and from the theoretical viewpoint (eg., because of the UV incompleteness of quantized Einstein gravity, and the need of its uniﬁcation with the Standard Model of Elementary Particles). In our approach, the origin of inﬂation is purely geometrical, ie. is closely related to spacetime and gravity.
0p lulaula 25102012 30 8 Download

Invariant measures for the geodesic ﬂow on the unit tangent bundle of a negatively curved Riemannian manifold are a basic and wellstudied subject. This paper continues an investigation into a 2dimensional analog of this ﬂow for a 3manifold N . Namely, the article discusses 2dimensional surfaces immersed into N whose product of principal curvature equals a constant k between 0 and 1, surfaces which are called ksurfaces.
37p noel_noel 17012013 20 4 Download

There are very few examples of Riemannian manifolds with positive sectional curvature known. In fact in dimensions above 24 all known examples are diﬀeomorphic to locally rank one symmetric spaces. We give a partial explanation of this phenomenon by showing that a positively curved, simply connected, compact manifold (M, g) is up to homotopy given by a rank one symmetric space, provided that its isometry group Iso(M, g) is large. More precisely we prove ﬁrst that if dim(Iso(M, g)) ≥ 2 dim(M ) − 6, then M is tangentially homotopically equivalent to a rank one symmetric space or M...
63p noel_noel 17012013 25 4 Download

Chúng tôi nghiên cứu đóng submanifolds M kích thước 2n + 1, đắm mình vào một (4N + 1) chiều Sasakian hình thức không gian (N, ξ, η, φ) với c cong φcắt liên tục, như vậy mà lĩnh vực vector Reeb ξ là tiếp tuyếnM.
12p phalinh21 01092011 19 2 Download

Introduction to Differential Geometry and General Relativity Lecture Notes by Stefan Waner, with a Special Guest Lecture by Gregory C. Levine Department of Mathematics, Hofstra University These notes are dedicated to the memory of Hanno Rund. TABLE OF CONTENTS 1. Preliminaries: Distance, Open Sets, Parametric Surfaces and Smooth Functions 2. Smooth Manifolds and Scalar Fields 3. Tangent Vectors and the Tangent Space 4. Contravariant and Covariant Vector Fields 5. Tensor Fields 6. Riemannian Manifolds 7. Locally Minkowskian Manifolds: An Introduction to Relativity 8.
128p khangoc2391 11082012 21 1 Download

This work develops the geometry and dynamics of mechanical systems with nonholonomic constraints and symmetry from the perspective of Lagrangian me chanics and with a view to controltheoretical applications. The basic methodology is that of geometric mechanics applied to the Lagranged’Alembert formulation, generalizing the use of connections and momentum maps associated with a given symmetry group to this case.
79p loixinloi 08052013 14 1 Download