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arXiv · 1304.2937

A compactness theorem in Finsler geometry

Mihai Anastasiei·Ioan Radu Peter
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Abstract

Let (M.F) be a complete Finsler manifold and P be a minimal and compact submanifold of M. Ric_k(x), x in M is a differential invariant that interpolates between the flag curvature and the Ricci curvature. We prove that if on any geodesic c(t) emanating orthogonally from P we have \int_{0}^{\infty}\mathbf{Ric}_{k}(t)>0, then M is compact.

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Mihai Anastasiei, Ioan Radu Peter. 2013-04-10. A compactness theorem in Finsler geometry. https://arxiv.org/abs/1304.2937

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