Riemannian Geometry: Some Examples, including Map Projections

نویسنده

  • SVANTE JANSON
چکیده

Some standard formulas are collected on curvature in Riemannian geometry, using coordinates. (There are, as far as I know, no new results). Many examples are given, in particular for manifolds with constant curvature, including many well-known map projections of the sphere and several well-known representations of hyperbolic space, but also some lesser known.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Sub-Riemannian Geometry: Basic Ideas and Examples

This tutorial serves as an introduction to the basic ideas in sub-Riemannian geometry. The discussion emphasizes the relevance of this subject from a control theoretic point of view. Some examples of sub-Riemannian geometries such as the Heisenberg geometry and other Carnot groups have also been given.

متن کامل

Identification of Riemannian foliations on the tangent bundle via SODE structure

The geometry of a system of second order differential equations is the geometry of a semispray, which is a globally defined vector field on TM. The metrizability of a given semispray is of special importance. In this paper, the metric associated with the semispray S is applied in order to study some types of foliations on the tangent bundle which are compatible with SODE structure. Indeed, suff...

متن کامل

Minimal Graphs in H × R and Their Projections

June 29, 2007 There has been a recent resurgence of interest in the subject of minimal surfaces in product three-manifolds, for example H ×R [Ros02], [MR04], [MIR05], [NR02], [Dan06], [FM05], [HET05]. The purpose of this note is to describe a construction and some examples originating in the harmonic maps literature whose consequences for minimal surfaces seem to have escaped notice. We organiz...

متن کامل

Hyperkähler Geometry and the Moduli Space of Higgs Bundles

Today will be mostly preliminaries, including some complex and symplectic geometry, such as the symplectic quotient, and an introduction to Kähler and hyperkähler geometry. Over the rest of the week, we’ll discuss some examples (which are usually left implicit) such as quiver varieties, introduce the moduli space of Higgs bundles, and more. A good reference for this is Andy Neitzke’s lecture no...

متن کامل

The Hopf-rinow Theorem

This paper is an introduction to Riemannian geometry, with an aim towards proving the Hopf-Rinow theorem on complete Riemannian manifolds. We assume knowledge of the basics of smooth manifolds, including the tangent and cotangent bundles and vector fields. After a brief introduction to tensors, we develop the foundations of Riemannian geometry: geodesics, the exponential map, and the Riemannian...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2015