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- H Rademacher
- Proceedings of the National Academy of Sciences…
- 1937

For non-reversible Finsler metrics of positive flag curvature on spheres and projective spaces we present results about the number and the length of closed geodesics and about their stability properties.

We show the existence of at least two geometrically distinct closed geodesics on an n-dimensional sphere with a bumpy and non-reversible Finsler metric for n > 2.

We give a lower bound for the length of a non-trivial geodesic loop on a simply-connected and compact manifold of even dimension with a non-reversible Finsler metric of positive flag curvature. Harris and Paternain use this estimate in their recent paper [HP] to give a geometric characterization of dynamically convex Finsler metrics on the 2-sphere. On… (More)

We consider a submanifold M of a Riemannian manifold (M , g). The Riemannian metric g induces a Riemannian metric g on the submanifold M. Then (M, g) is also called a Riemannian submanifold of the Riemannian manifold (M , g). Definition 1.1. A submanifold M of a Riemannian manifold (M , g) is called totally geodesic if any geodesic on the submanifold M with… (More)

We show the existence of at least two geometrically distinct closed geodesics on an n-dimensional sphere with a bumpy and non-reversible Finsler metric for n > 2.

- Wolfgang K, Hans-Bert Rademacher, Wolfgang K Uhnel, Hans{bert Rademacher
- 1997

Based on the Berger{Simons holonomy classiication, we classify all Rie-mannian spin manifolds carrying a twistor spinor with at least one zero. In particular, the dimension n of the manifold is either even or n = 7. The metric is conformal to either a at metric or a Ricci at and locally irreducible metric.

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