The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Surface geodesics
Replies: 16   Last Post: Jan 23, 2014 7:01 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]

Posts: 9
Registered: 1/19/14
Re: Surface geodesics
Posted: Jan 22, 2014 7:42 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

This is by far the best answer and it comes with a reference, so THANK YOU VERY
MUCH. I'll take a look at that book if I can get my hands on it.

On 22/01/2014 01:17, Leon Aigret wrote:
> On Sun, 19 Jan 2014 17:40:23 +0100, ?XPOSITO <>
> wrote:

>> Can somebody provide an example of a connected surface containing **NO**
>> non-plane geodesics,
>> apart from those surfaces contained in the plane or the sphere?

> Probably not. Theorem 6.7.1 at the bottom of page 74 in Differential
> and Riemannian Geometry by Detlev Laugwitz states:
> If all geodesics of a surface are plane curves then the surface is a
> piece of a sphere or of the plane.
> Leon

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.