Some Geodesics in Open Surfaces Classified by Clairaut's Relation

In this paper, we studied some properties of geodesic on some open surfaces: Hyperboloid, Paraboloid and Funnel Surface. Geodesic equation in the v-Clairaut parameterization was calculated and reduced to definite integral. Some geodesics on some open surfaces as mention above were classified by Clairaut's relation.

• Wongvisarut Khuangsatung
• Pakkinee Chitsakul

• Geodesic
• Surface of revolution
• Clairaut's relation
• Clairaut parameterization.

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