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Sunday, August 9, 2020 | History

3 edition of **Spaces with distinguished geodesics** found in the catalog.

Spaces with distinguished geodesics

Herbert Busemann

- 85 Want to read
- 5 Currently reading

Published
**1987**
by M. Dekker in New York
.

Written in English

- G-spaces.,
- Geodesics (Mathematics)

**Edition Notes**

Statement | Herbert Busemann, B.B. Phadke. |

Series | Monographs and textbooks in pure and applied mathematics ;, 108 |

Contributions | Phadke, B. B. 1944- |

Classifications | |
---|---|

LC Classifications | QA689 .B83 1987 |

The Physical Object | |

Pagination | viii, 159 p. : |

Number of Pages | 159 |

ID Numbers | |

Open Library | OL2376907M |

ISBN 10 | 0824775457 |

LC Control Number | 87005265 |

A synthetic approach to intrinsic differential geometry in the large and its connections with the foundations of geometry was presented in "The Geometry of Geodesics" (, quoted as G). It is the purpose of the present report to bring this theory up to date. Many of the later ations were stimulated by problems posed in G, others concern newtopics. A comprehensive approach to qualitative problems in intrinsic differential geometry, this text for upper-level undergraduates and graduate students emphasizes cases in which geodesics possess only local uniqueness properties--and consequently, the relations to the foundations of geometry are decidedly less relevant, and Finsler spaces become the principal s: 1.

data space has more than one dimension, then the data values are vector mea surements. For example, weather data may include temperature and pressure (two-dimensional vector measurements) in the three-dimensional coordinate space of longitude, latitude, and . This book provides an introduction to the differential geometry of curves and surfaces in three-dimensional Euclidean space and to n-dimensional Riemannian geometry. Based on Kreyszig's earlier book Differential Geometry, it is presented in a simple and understandable manner with many examples illustrating the ideas, methods, and results.

Get this from a library! The geometry of geodesics. [Herbert Busemann] -- This volume is concerned with a geometric approach to qualitative problems in intrinsic differential geometry, with an emphasis on spaces in which the geodesics have only local uniqueness properties. euler equation and geodesics 4 We note that if J[u + eh] has a local extremum at u, then u is a stationary function for J. This will occur when df de e=0 0. x f(x) (x 1,y 1) (x2,y2) Figure 2: Paths near an optimal path between two ﬁxed points.

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Spaces With Distinguished Geodesics | Herbert Busemann, B. Phadke | download | B–OK. Download books for free. Find books. Additional Physical Format: Online version: Busemann, Herbert, Spaces with distinguished geodesics.

New York: M. Dekker, © (OCoLC) Download E-books Spaces With Distinguished Geodesics (Pure and Applied Mathematics) PDF. Janu admin. By Herbert Busemann. Show description. Read or Download Spaces With Distinguished Geodesics (Pure and Applied Mathematics) PDF. Best Differential Geometry books/5(48).

Herbert Busemann (12 May – 3 February ) was a German-American mathematician specializing in convex and differential is the author of Busemann's theorem in Euclidean geometry and geometric was a member of the Royal Danish Academy and a winner of the Lobachevsky Medal (), the first American mathematician to receive it.

In the framework of jet spaces endowed with a non-linear connection, the special curves of these spaces (h-paths, v-paths, stationary curves and geodesics) which extend the corresponding notions from Riemannian geometry are characterized.

The main geometric objects and the paths are described and, in the case when the vertical metric is independent of fiber coordinates, the first two Cited by: 1. This work is devoted to results on the G-spaces of Busemann found after the appearance of his book "The Geometry of Geodesics" (Academic Press, New York, ); and denoted here as.

The space of geodesics may inherit additional structure from the structure of the manifold: for example Hitchin looks at the complex structure of the space of geodesics of ${\mathbb R}^3$ to study monopoles and minimal surfaces in Monopoles and geodesics, Comm.

Math. Phys. Vol Number 4. The Geometry of Geodesics, Academic Press, New York, zbMATH Google Scholar [BuPh87] Busemann H. and Phadke B.B. Spaces with Distinguished Geodesics, Marcel Dekker, New York, zbMATH Google Scholar. A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text.

We also show that the number of simple closed geodesics of length L on X E Mg,n has the asymptotic behavior sx(L) rv nxL6g-6+n as L We relate the function nx to the geometry of X and intersection theory on moduli spaces of curves, and calculate the frequencies of different types of simple closed geodesics on a hyperbolic surface.

asserts that, on the two-dimensional real-projective space, a riemannian structure all of whose geodesics are closed has to be isometric to the standard one, and the theorem of E.

Hopf: on the two-dimensional torus, a riemannian structure all of whose geodesics are without conju-gate points has to be a ﬂat one. As a counterpoint we have quote. metric space there exist distinguished geodesics that satisfy a weak global non-positive curvature condition.

More precisely, every injective metric space admits a conical geodesic bicombing. A geodesic bicombing on a metric space (X,d) is a map σ: X×X×[0,1] → X such that σxy():= σ(x,y,) is a metric geodesic from x to y for any pair. Injective metric spaces, or absolute 1-Lipschitz retracts, share a number of properties with CAT(0) spaces.

In the '60s Isbell showed that every metric space X has an injective hull E (X). Here it is proved that if X is the vertex set of a connected locally finite graph with a uniform stability property of intervals, then E (X) is a locally finite polyhedral complex with finitely many isometry.

In these spaces geodesics going through a point are generated by the action of the horizontal one-parameter subgroups of the acting Lie group on that point [32,36,39]. In our case the one-parameter subgroups of the linear group are the curves exp (t A) for t ∈ R, and the horizontal vectors are the symmetric matrices A = A ⊤ ∈ sim.

Other articles where Geodesic is discussed: relativity: Curved space-time and geometric gravitation: the shortest natural paths, or geodesics—much as the shortest path between any two points on Earth is not a straight line, which cannot be constructed on that curved surface, but the arc of a great circle route.

In Einstein’s theory, space-time geodesics define the deflection of light. The space of oriented polygonal shapes PS (n) is the space of polygons with n distinguished vertices up to equivalence by orientation-preserving similarity; that is, two polygons (z 1,z n) and (w 1,w n) are identified if and only if there exists a complex affine transformation f (z) = a z + b of C, a ≠ 0, so that f (z k) = w k for.

He was the author of numerous books, including Convex Surfaces and, with B.B. Phadke, Spaces With Distinguished Geodesics. A native of Berlin, Busemann earned his Ph.D. in mathematics from the. In mathematics, a hyperbolic space is a homogeneous space that has a constant negative curvature, where in this case the curvature is the sectional is hyperbolic geometry in more than 2 dimensions, and is distinguished from Euclidean spaces with zero curvature that define the Euclidean geometry, and elliptic geometry that have a constant positive curvature.

Geodesics on Riemannian Manifolds Geodesics, Local Existence and Uniqueness If (M,g)isaRiemannianmanifold,thentheconceptof length makes sense for anypiecewise smooth (in fact, C1) curve on M.

Then, it possible to deﬁne the structure of a metric space on M,whered(p,q)isthegreatestlowerboundofthe length of all curves joining p and q. The Geometry of Geodesics - Ebook written by Herbert Busemann.

Read this book using Google Play Books app on your PC, android, iOS devices. Download for offline reading, highlight, bookmark or take notes while you read The Geometry of Geodesics. Spaces with distinguished geodesics by Herbert Busemann.

First published in 1 edition. Not in Library. Introduction to algebraic manifolds by Differential Geometry, Accessible book, Convex surfaces, Curves on surfaces, Geodesics.(x;y) 2X X. The convention to call a collection of paths of a metric space bicombing is due to Epstein and Thurston [16, p].

The study of metric spaces with distinguished geodesics goes back to the work of Busemann [4]. To streamline the terminology, from now on, bicombing will mean geodesic.Geodesic definition, pertaining to the geometry of curved surfaces, in which geodesic lines take the place of the straight lines of plane geometry.

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