Ebooks May 29, 2022 1
The main topic of these notes is geodesics. Our aim is 1) to give a fairly complete treatment of the foundations of Riemannian geometry through the tangent
Ebooks May 29, 2022 2
These lecture notes in Lie Groups are designed for a 1-semester third year or graduate course in mathematics, physics, engineering, chemistry or biology.
Medians and Means in Riemannian Geometry: Existence, Uniqueness and Computation by M. Arnaudon, F. Barbaresco, L. Yang
Ebooks May 28, 2022 2
This paper is a short summary of our recent work on the medians and means of probability measures in Riemannian manifolds. Firstly, the existence and uniqueness results of local medians are given. In order to compute medians in practical cases, we propose a subgradient algorithm and prove its convergence....
Ebooks May 28, 2022 3
Contents: Differential Calculus; Differentiable Bundles; Connections on Principal Bundles; Holonomy Groups; Vector Bundles and Derivation Laws; Holomorphic Connections (Complex vector bundles, Almost complex manifolds, Derivation law in the complex case).
Ebooks May 27, 2022 3
This textbook can be used as a non-technical and geometric gateway to many aspects of differential geometry. The audience of the book is anybody with a reasonable mathematical maturity, who wants to learn some differential geometry.
Ebooks May 27, 2022 6
These notes give an introduction to embedded contact homology (ECH) of contact three-manifolds, gathering together many basic notions which are scattered across a number of papers.
Ebooks May 27, 2022 5
We shall consider some heterogeneous topics relating to Lie groups and the general theory of representations of locally compact groups. The first part exclusively deals with some elementary facts about Lie groups and the last two parts are entirely independent of the material contained in the first. ...
Ebooks May 27, 2022 2
Contents: Ricci-Hamilton flow on surfaces; Bartz-Struwe-Ye estimate; Hamilton's another proof on S2; Perelman's W-functional and its applications; Ricci-Hamilton flow on Riemannian manifolds; The maximum principles; Curve shortening flow on manifolds; Selected topics in Nirenberg's problem.
Ebooks May 26, 2022 2
The book emphasizes the most useful aspects of Lie groups, in a way that is easy for students to acquire and to assimilate. It includes a chapter dedicated to the applications of Lie group theory to solving differential equations.
Ebooks May 26, 2022 3
A new synthesis of the principles of quantum mechanics and Relativity is proposed in the context of complex differential geometry. The positivity of the energy implies that wave functions and fields can be extended to complex spacetime.