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Circles in compact homogeneous Riemannian spaces and immersions of finite type

Published online by Cambridge University Press:  18 July 2002

Bang-Yen Chen
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, MI 48824-1027, U.S.A. e-mail: bychen@math.msu.edu
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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.

Type
Research Article
Copyright
2002 Glasgow Mathematical Journal Trust

Footnotes

Dedicated to Professor Koichi Ogiue on the occasion of his sixtieth birthday.