Download A Treatise on the Differential Geometry of Curves and by Luther Pfahler Eisenhart PDF

By Luther Pfahler Eisenhart

Created particularly for graduate scholars, this introductory treatise on differential geometry has been a hugely winning textbook for a few years. Its surprisingly particular and urban strategy features a thorough clarification of the geometry of curves and surfaces, focusing on difficulties that would be such a lot priceless to scholars. 1909 version.

Show description

Read or Download A Treatise on the Differential Geometry of Curves and Surfaces PDF

Similar differential geometry books

Transformation Groups in Differential Geometry

Given a mathematical constitution, one of many easy linked mathematical gadgets is its automorphism team. the article of this e-book is to provide a biased account of automorphism teams of differential geometric struc­ tures. All geometric buildings aren't created equivalent; a few are creations of ~ods whereas others are items of lesser human minds.

The Geometry of Physics

This booklet presents a operating wisdom of these elements of external differential kinds, differential geometry, algebraic and differential topology, Lie teams, vector bundles, and Chern types which are necessary for a deeper knowing of either classical and glossy physics and engineering. it really is perfect for graduate and complicated undergraduate scholars of physics, engineering or arithmetic as a path textual content or for self learn.

Modern geometry. Part 2. The geometry and topology of manifolds

This can be the 1st quantity of a three-volume creation to trendy geometry, with emphasis on purposes to different parts of arithmetic and theoretical physics. issues coated comprise tensors and their differential calculus, the calculus of adaptations in a single and a number of other dimensions, and geometric box idea.

Advances in Discrete Differential Geometry

This is often one of many first books on a newly rising box of discrete differential geometry and a very good approach to entry this interesting quarter. It surveys the attention-grabbing connections among discrete types in differential geometry and complicated research, integrable structures and purposes in special effects.

Additional resources for A Treatise on the Differential Geometry of Curves and Surfaces

Example text

M find that the distance to second order at most. TJie osculating crossed ~by nearest to the From plane the curve, a twisted curve at an ordinary point to and of all the planes through the point is it lies curve. the second of (53) seen that y is positive for suffior positive negative. Hence, in the neighborhood of an ordinary point, the curve lies entirely on one side of the plane determined by the tangent and binormal on ciently small values of it is , the side of the positive direction of the principal normal.

P; hence the center of the sphere tiated, we get t\ = If this equation be differenon the polar line for each is Another differentiation gives, together with the preceding, the following coordinates of the center of the sphere point. : 1=0, (91) When the last of these equations (92) , is J Conversely, when = P> f = -Tp'. differentiated + we obtain the desired condition (rpO'=0. this condition is satisfied, the point with the coordinates (91) is lies and at constant distance from points of the curve.

Determine the order of the minimal curves for which the function /in (113) satisfies the condition 5. A (X + B* + C2 = 0. A plane whose equation is that the osculating plane of a minimal curve can be written B + (Z Show 4/'"/v __ 5/1*2 = o. that the equations of a minimal curve, for which /in (113) satisfies the 5/lv2 = c/'"8 , where a is a constant, can be put in the form condition 4/"'/ v x = 8 cos i, = 8- sin . y . z i, = 8*. t. GENERAL EXAMPLES 1. Show that the equations of any plane curve can be put in the form x = Jcos 0/(#) cfy, y and determine the geometrical significance of 2.

Download PDF sample

Rated 4.94 of 5 – based on 23 votes
 

Author: admin