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Dergiler / International Electronic Journal of Geometry / 2026 / Volume: 14 Issue: 1

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

Issa A. Kaboye(Université de Zinder)
Mahamane Mahi Harouna(Université Dan Dicko Dankoulodo de Maradi)
Mahaman Bazanfaré(Université Abdou Moumouni de Niamey)0000-0002-8085-2830
Sayfa
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Yayın Tarihi
2021-04-15
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

We also prove a volume comparison theorem for such manifolds.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper we establish some new compactness criteria for complete Riemannian manifolds with Bakry-\'Emery Ricci curvature bounded below.
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Temel Bulgular & Veri:These results improve or generalize previous ones obtained by H.
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Sonuç & Katkı:We also prove a volume comparison theorem for such manifolds.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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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Bu Makaleye Atıf Yap

Kaboye, I. A., Harouna, M. M., Bazanfaré, M. (2021). Some Myers-Type Theorems and Comparison Theorems for Manifolds with Modified Ricci Curvature. International Electronic Journal of Geometry, Volume: 14 Issue: 1. https://doi.org/10.36890/iejg.819887

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Kaynakça (9)

  1. Bazanfaré, M.: A volume comparison theorem and number of ends for manifolds with asymptotically nonnegative Ricci curvature. Revista Math. Compl. 13-2, 399–409 (2000).
  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).