Zhang Ya-yang
Abstract
The paper discusses the existence and geometric properties of conjugate points of the geodesics in a complete Riemannian manifold,and proves that for a complete geodesic γ:(-∞,+∞)→M,if k(∧v)≥0,then γ is a geodesic without conjugate points if and only if k(∧v)=0.
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The paper discusses the existence and geometric properties of conjugate points of the geodesics in a complete Riemannian manifold,and proves that for a complete geodesic γ:(-∞,+∞)→M,if k(∧v)≥0,then γ is a geodesic without conjugate points if and only if k(∧v)=0.
Key concepts: Conjugate points, Geodesic, Riemannian manifold, Mathematics, Manifold (fluid mechanics), Geodesic map, Pure mathematics, Conjugate