Geodesic
Circles in compact homogeneous Riemannian spaces and immersions of finite type
Glasgow mathematical journal, Tome 44 (2002) no. 1, pp. 93-102

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A unit speed curve \gamma =\gamma (s) in a Riemannian manifold N is called a circle if there exists a unit vector field Y(s) along \gamma and a positive constant k such that \nabla _s \gamma '(s)=k Y(s),\, \nabla _s Y(s)=-k \gamma '(s). The main purpose of this article is to investigate the fundamental relationships between circles, maximal tori in compact symmetric spaces, and immersions of finite type. 
Chen, Bang-Yen. Circles in compact homogeneous Riemannian spaces and immersions of finite type. Glasgow mathematical journal, Tome 44 (2002) no. 1, pp. 93-102. doi: 10.1017/S0017089502010054
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