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

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Leon Aigret

Posts: 43
Registered: 12/5/13
Re: Surface geodesics
Posted: Jan 21, 2014 7:17 PM
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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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