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Journals / International Electronic Journal of Geometry / 2021 / Cilt: 14 - Sayı: 1

Some Myers-Type Theorems and Comparison Theorems for Manifolds with Modified Ricci Curvature

Issa A. KABOYE
Harouna M. MAHI
Mahaman BAZANFARÉ
Pages
174–182
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We also prove a volume comparison theorem for such manifolds.

📌 3 Key Takeaways

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Objective & Hypothesis:In this paper we establish some new compactness criteria for complete Riemannian manifolds with Bakry-\'Emery Ricci curvature bounded below.
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Key Findings & Data:These results improve or generalize previous ones obtained by H.
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Conclusion & Impact:We also prove a volume comparison theorem for such manifolds.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Bakry-Emery Ricci curvature · Myers-type theorem · Modified mean curvature

Abstract

In this paper we establish some new compactness criteria for complete Riemannian manifolds with Bakry-\'Emery Ricci curvature bounded below. These results improve or generalize previous ones obtained by H. Tadano [6], J. Wan [7], I.A. Kaboye and M. Bazanfar\'e [3]. We also prove a volume comparison theorem for such manifolds.

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Cite This Article

KABOYE, I. A., MAHI, H. M., BAZANFARÉ, M. (2022). Some Myers-Type Theorems and Comparison Theorems for Manifolds with Modified Ricci Curvature. International Electronic Journal of Geometry, Cilt: 14 - Sayı: 1, 174–182. https://ajindex.com/articles/539583

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References (9)

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  2. Galloway, G. J.: A generalization of Myers’ theorem and an application to relativistic cosmology. J. Differential Geom. 14-1, 105–116, (1979)
  3. Kaboye, I.A. and Bazanfaré, M.: Manifolds with Bakry-Émery Ricci Curvature Bounded Below. Advances in Pure Mathematics. 6, 754-764 (2016)
  4. Limoncu, M.: The Bakry-Émery Ricci tensor and its applications to some compactness theorems. Math. Z. 271, 715–722 (2012)
  5. Soylu, Y.: A Myers-type compactness theorem by the use of Bakry-Émery Ricci tensor. Differ. Geom. Appl. 54, 245–250 (2017)
  6. Tadano, H.: Some Ambrose and Galloway-type theorems via Bakry-Émery and modfied Ricci curvatures. Pacific J. Math. 294-1, 213-231 (2018)
  7. Wan, J.: An extension of Bonnet-Myers theorem. Math. Z. 291, 195–197 (2019)
  8. Wei, G. and Wylie, W.: Comparison geometry for the Bakry-Émery Ricci tensor. J. Differ. Geom. 83, 377–405 (2009)
  9. Wu, J.Y.: Myers’ type theorem with the Bakry-Émery Ricci tensor. Ann. Global Anal. Geom. 54-4, 541–549 (2018).