Download A Primer on Riemann Surfaces by A. F. Beardon PDF

By A. F. Beardon

Show description

Read Online or Download A Primer on Riemann Surfaces PDF

Best geometry books

Geometry of Banach spaces. Proc. conf. Strobl, 1989

This quantity displays the development made in lots of branches of contemporary learn in Banach area thought, an analytic method of geometry. together with papers through lots of the major figures within the region, it truly is meant to demonstrate the interaction of Banach house concept with harmonic research, likelihood, complicated functionality conception, and finite dimensional convexity concept.

Comparison Theorems in Riemannian Geometry

The vital topic of this booklet is the interplay among the curvature of a whole Riemannian manifold and its topology and worldwide geometry. the 1st 5 chapters are preparatory in nature. they start with a truly concise creation to Riemannian geometry, by way of an exposition of Toponogov's theorem--the first such remedy in a booklet in English.

Space, Time and Geometry

The articles during this quantity were prompted in alternative ways. greater than years in the past the editor of Synthese, laakko Hintikka, an­ nounced a different factor dedicated to house and time, and articles have been solicited. a part of the cause of that assertion was once additionally the second one resource of papers. numerous years in the past I gave a seminar on particular relativity at Stanford, and the papers via Domotor, Harrison, Hudgin, Latzer and myself in part arose out of debate in that seminar.

Geometry of Cauchy-Riemann Submanifolds

This booklet gathers contributions by way of revered specialists at the conception of isometric immersions among Riemannian manifolds, and specializes in the geometry of CR buildings on submanifolds in Hermitian manifolds. CR buildings are a package deal theoretic recast of the tangential Cauchy–Riemann equations in advanced research related to a number of advanced variables.

Extra info for A Primer on Riemann Surfaces

Example text

By taking B f are open and g open, we see that ifhis open then so is h then so is g. Finally, = gf. Exercise 2,7 1, Let generated by x that the map g G (x) b- exp(ix) G x + 2irand let of X/G into W be the group of translations of the real line f : X -► X/G be the natural map. Show = iz : |z| = l) defined by is properly defined and 1-1. Show that the composite map h : x h- exp(ix) is open, continuous and surjective and deduce that is homeomorphic to X/G W. 8 A BASE FOR A TOPOLOGY * Let B be a class of subsets of of those subsets of X of sets chosen from B.

It is a theorem (much later) and not an assumption that these conditions hold for a Riemann surface: this example merely serves to emphasize this result and is of no other importance. 6. First, define f : JR^ ‘►JR'* (x,y,z) if y < O? (x+^-,y,0) if y > O . f (x,y,z) Next, partition JR into the horizontal planes = i(x,y,z) e JR and define : z = t) by 38 S = f(IR3) = {(x,y,z) elR3 : y < 0} U PQ . Observe that f restriction of induced by so A f ffc. is acts on S to and let We give T-open as the identity map.

If the charts S S is a surface and has a natural concept of (for example, if a : S -*■ S is a smooth preserve angles (in sense and magnitude) then the same is true of all transition functions. 2) and so S is actually a Riemann surface. To summarise, a surface is a Riemann surface if angles can be defined on the surface and if the charts a are angle-preserving. We obtain even greater flexibility if we allow the angles at points region U^. x provided that each x a If this is so, the only transition function defined at is the identity (= to distort lies in only one parametric and so the distortion of angles at x a (x) cannot violate the requirement for a Riemann surface.

Download PDF sample

Rated 4.51 of 5 – based on 38 votes