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

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€XPOSITO

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 <expotroll@yogurazo.com>
> 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
>




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