A Note on the Generalized Myers Theorem for Finsler Manifolds

Wu, Bing-Ye

doi:10.4134/bkms.2013.50.3.833

Cited by 12 publications

(6 citation statements)

References 7 publications

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“…Remark 2.1. If in the main theorem (Theorem 1.2) from [15] the function max is explicitly written, two statements are obtained. The one covers the first three items of the Bonnet-Myers theorem.…”

Section: Proof Of Theorem Amentioning

confidence: 99%

Some remarks on Myers theorem for Finsler manifolds

Anastasiei

2014

Preprint

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The standard Bonnet-Myers theorem says that if the Ricci scalar of a Riemannian manifold is bounded below by a positive number, then the manifold is compact. Moreover, a bound of its diameter is pointed out. The theorem was extended to Finsler manifolds. In this paper we prove that if a certain condition on the average of the Ricci scalar holds, then the Finsler manifold M is compact if the Ricci scalar is bounded above by the same positive number. An upper bound of the diameter is also found. With no condition on Ricci scalar itself but with a different one on its average, we find that the Finsler manifold M is again compact. This time no bound of the diameter is found.The proofs are given in the Finslerian setting and are based on the index form along geodesics.Mathematics Subject Classification 2000: 53C60.

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Section: Proof Of Theorem Amentioning

confidence: 99%

Some remarks on Myers theorem for Finsler manifolds

Anastasiei

2014

Preprint

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“…The recent works have shown that some well-known results in Riemannian geometry have been extended to the Finsler setting. For examples in this scope, the reader is referred to [1][2][3] and references therein. In the Riemannian case, Ambrose [4] proved a compactness theorem by a condition on the integral of Ricci tensor along geodesics.…”

Section: Introductionmentioning

confidence: 99%

Ambrose Teoreminin Finsler Versiyonu Üzerine Bir Not

Soylu

2020

Bitlis Eren Üniversitesi Fen Bilimleri Dergisi

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“…The recent works have shown that some results in Riemannian geometry have been extended to the Finsler setting. For example in this scope, the reader is referred to [1,2,3] and references therein.…”

Section: Introductionmentioning

confidence: 99%