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Helgason spheres of compact symmetric spaces and immersions of finite type
Published online by Cambridge University Press: 17 April 2009
Abstract
A unit speed curve γ = γ(s) in a Riemannian manifold N is called a circle if there exists a unit vector field Y(s) along γ and a positive constant k such that ∇sγ′(s) = kY(s), ∇sY(s) = −kγ′(s). A maximal totally geodesic sphere with maximal sectional curvature in a compact irreducible symmetric space M is called a Helgason sphere. A circle which lies in a Helgason sphere of a compact symmetric space is called a Helgason circle. In this article we establish some fundamental relationships between Helgason circles, Helgason spheres of irreducible symmetric spaces of compact type and the theory of immersions of finite type.
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- Copyright © Australian Mathematical Society 2001